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American and Soviet Research 

Edited by 

Thomas M. Donahue 


Kathleen Kearney TYivers 
David M. Abramson 

Proceedings from the US-USSR Workshop 


Planetary Sciences 

January 2-6, 1989 

Academy of Sciences of the Union of Soviet Socialist Republics 
National Academy of Sciences of the United States of America 

National Academy Press 
Washington, D.C. 1991 

NOTICE: The project that is the subject of this report was approved by the officers of the 
National Academy of Sciences and the Academy of Sciences of the USSR on January 12, 1988. The 
members of the committee responsible for the report were chosen for their special competences and 
with regard for appropriate balance. 

This report has been reviewed by a group other than the authors according to procedures 
approved by a Report Review Committee consisting of members of the National Academy of 
Sciences, the National Academy of Engineering, and the Institute of Medicine. 

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on scientific and technical matters. Dr. Frank Press is president of the National Academy of Sciences. 

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Library of Congress Catalog Card No. 90-62812 
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The Academy of Sciences of the USSR and the National Academy 
of Sciences of the United States of America sponsored a workshop on 
Planetary Sciences at the Institute for Space Research in Moscow, January 
2-6, 1989. The purpose of the workshop, which was attended by Soviet and 
American scientists, was to examine the current state of our theoretical 
understanding of how the planets were formed and how they evolved to 
their present state. The workshop assessed the type of observations and 
experiments that are needed to advance understanding of the formation and 
evolution of the solar system based on the current theoretical framework. 

In the past, models of the formation and evolution of the planets have 
been just that, models. They essentially portrayed possibilities: that events 
could have transpired in the way depicted without violating any known 
constraints and that, if they did take place, certain consequences would 
follow. Now, we may be advancing beyond that stage to the point where it 
may be possible to settle fairly definitely on certain scenarios and exclude 
others. Assessment of the present state of theories and the observational 
base will help determine the extent to which this is the case. 

This workshop focused on the present status of observational and 
theoretical understanding of the clearing of stellar nebulae, planetesimal 
formation, and planetary accretion; the evolution of atmospheres; the rela- 
tionship of still existing primitive bodies to these topics; and the relationship 
of ground-based and in situ measurements. 

As the papers presented at the workshop and published in this volume 
show, astronomical observations are now at hand that will reveal the 
sequence of events occuring in circumstellar disks with sufTicient precision 
to define the models of planetary formation. Moreover, theories for the 
origin of the solar system have reached a point where it is now possible, 


indeed it is essential, to examine them in the broader context of the origins 
of planetary systems. Until recently, it has not been possible to select among 
a range of feasible scenarios the one that is most likely to be correct, in 
the sense that it satisfies observational and theoretical constraints. We are 
now advancing to that stage. 

Similarly, theories for the formation of planetary atmospheres are 
becoming more sophisticated and respond to an increasingly complex set 
of observational data on relative abundance of atmospheric species and the 
state of degassing of the interior of the Earth. But, as the papers presented 
here will demonstrate, there is still a way to go before all the questions are 

The topics discussed at this workshop were timely, and the debate and 
discussion were full and informative. The participants learned a great deal, 
and the scientific basis for cooperation in planetary sciences was strength- 
ened appreciably. The Soviet hosts extended their usual thoughtful and 
gracious hospitality to the American delegation, and the entire experience 
was memorable and rewarding. 

T.M. Donahue 

Chairman, NAS/NRC Committee on 
Cooperation with the USSR on 
Planetary Science 



Financial support from Ni^A for the workshop and proceedings is 
gratefully acknowledged. The translation of the Soviet presentations for 
this publication by Dwight Roesch is also acknowledged and appreciated. 




Thomas M. Donahue 



Stephen E. Strom, Susan Edwards, Karen M. Strom 



Peter H. Bodenheimer 


Alan P. Boss 


Tamara V Ruzmaikina and AS. Makalkin 


Avgusta K. Lavrukhina 





Eugene H. Levy 


Stuart J. Weidenschilling 


George W. Wetherill 



Viktor S. Safronov 


Robert D. Gehrz 



Andrey V Vityazev and G.V, Pechemikova 



David J. Stevenson 


Vladimir N. Zharkov and VS. Solomatov 

14. DEGASSING 191 

James C.G. Walker 



Lev M. Mukhin and M.V Gerasimov 



Vladislav P. Volkov 



James F. Kasting 


Leonid S. Marochnik, Lev M. Mukhin, and Roald Z. Sagdeev 


Roald Z. Sagdeev and G.M. Zaslavskiy 


Robert A Brown 


List of Participants 


List of Presentations 



The Properties and Environment of Primitive 

Solar Nebulae as Deduced from Observations of 

Solar-Type Pre-main Sequence Stars^ 

Stephen E. Strom 

SuzAN Edwards^ 

Karen M. Strom 

University of Massachusetts, Amherst 


This contribution reviews a) current observational evidence for the 
presence of circumstellar disks associated with solar type pre-main sequence 
(PMS) stars, b) the properties of such disks, and c) the disk environment. 
The best evidence suggests that at least 60% of stars with ages t < 3 x 10^ 
years are surrounded by disks of sizes ~ 10 to 100 AU and masses ~ 0.01 to 
0.1 Mq. Because there are no known main sequence stars surrounded by 
this much distributed matter, disks surrounding newborn stars must evolve 
to a more tenuous state. The time scales for disk survival as massive (M 
~ 0.01 to 0.1 Mq), optically thick structures appear to lie in the range t 
< 3 X 10^ years to t ~ 10^ years. At present, this represents the best 
astrophysical constraint on the time scale for assembling planetary systems 
from distributed material in circumstellar disks. The infrared spectra of 
some solar-type PMS stars seem to provide evidence of inner disk clearing, 
perhaps indicating the onset of planet-building. 

The material in disks may be bombarded by energetic (~ 1 kev) 
particles from stellar winds driven by pre-main sequence stars. However, 
it is not known at present whether, or for how long such winds leave the 
stars a) as highly collimated polar streams which do not interact with disk 
material, or b) as more isotropic outflows. 

'Based in part on a review presented at the Space Telescope Science Institute Worlishop: 
The Formation and Evolution of Planetary Systems, Cambridge University Press (in press). 
^ Also at Smith College, Northampton, Massachusetts. 



Recent theoretical and observational work suggests that the process of 
star formation for single stars of low and intermediate mass (0.1 < M/M© 
< 5) results naturalfy in the formation of a circumstellar disk, which may 
then evolve to form a planetary system. This process appears to involve 
the following steps (Shu et al. 1987): 

• The formation of opaque, cold, rotating protostellar "cores" within 
larger molecular cloud complexes; 

• The collapse of a core when self-gravity exceeds internal pressure 

• The formation within the core of a central star surrounded by 
a massive (0.01 to 0.1 M©) circumstellar disk (embedded infrared source 
stage). At this stage, the star/disk system is surrounded by an optically 
opaque, infalling protostellar envelope. Gas and dust in the envelope rains 
in upon both the central stellar core and the surrounding disk, thus in- 
creasing both the disk and stellar mass. Infall of low angular momentum 
material directly onto the central star and accretion of high angular mo- 
mentum material through the disk provide the dominant contributions to 
the young stellar object's (YSO) luminosity, far exceeding the luminosity 
produced by gravitational contraction of the stellar core. Because the in- 
falling envelope is optically opaque, such YSOs can be observed only at 
wavelengths A > l/i. They exhibit infrared spectral energy distributions, 
AFa vs. a, which are a) broad compared to a blackbody distribution and 
b) flat, or rising toward long wavelengths (see Figure la). At some time 
during the infall phase, the central PMS star begins to drive an energetic 
wind (L^ind ~ 0.1 L,; Vwind ~ 200 kilometers per second). This is first 
observable as a highly collimated "molecular outflow" as it transfers mo- 
mentum to the surrounding protostellar and molecular cloud material and 
later (in some cases) as a "stellar jet" (Edwards and Strom 1988). TTie wind 
momentum is sufficient to reverse infaU from the protostellar envelope and 
eventually dissipates this opaque cocoon, thus revealing the YSO at visible 
wavelengths (Shu et al. 1987). 

• The optical appearance of a young stellar object (YSO) whose 
luminosity may be dominated in the infrared by accretion through the disk, 
and in the ultraviolet and optical region, by emission from a hot "boundary 
layer" (continuum + emission TTS phase). Accretion of material through 
the still massive (0.01 to 0.1 Mq) disk produces infrared continuum ra- 
diation with a total luminosity > 0.5 times the stellar luminosity. At 
this stage, the infrared spectrum is still much broader than a single, black- 
body spectrum (Myers et al, 1987; Adams etal. 1986), and in most cases falls 




^ -10 




S* -11 - 




.5 1 

log X(^M) 


.5 1 

log X{\iM} 


FIGURE 1 (a) A plot of the observed spectral energy distribution for the embedded 
infrared source, L1551/IRS 5. This source drives a well-studied, highly-collimated, bipolar 
molecular outflow and a stellar jet. Note that the spectrum rises toward longer wavelength, 
suggesting that IRS 5 is surrounded by a flattened distribution of circumstellar matter, 
possible remnant material from the protostellar core from which this YSO was assembled, 
(b) A plot of the observed spectral energy distribution for the continuum + emrrussion T 
Tauri suit, HL Tiu. Near-infrared images of HL "Ihu suggest that this YSO is surrounded 
by a flattened distribution of circumstellar dust. Its infrared spectrum is nearly fiat, which 
suggests that HL "Biu is as well still surrounded by a remnant, partially opaque envelope. 


toward longer wavelengths. In a few cases, the spectrum is flat or rises 
toward long wavelengths, perhaps reflecting the presence of a partiaUy 
opaque, remnant infalling envelope (Figure lb). 

The accretion of material from the rapidly rotating (~ 200 kilometers 
per second), inner regions of the disk to the slowly rotating (~ 20 kilometers 
per second) stellar photosphere also produces a narrow, hot (T > 8000 
K) emission region: the "boundary layer" (Kenyon and Hartmann 1987; 
Bertout et al. 1988). Radiation from the boundary layer overwhelms that 
from the cool PMS star photosphere. Consequentty, the photospheric 
absorption spectrum cannot be seen against the boundary layer emission at 
A < 7000 A. Strong permitted and forbidden emission lines (perhaps tracing 
emission associated with energetic stellar winds and the boundary layer) 
are also present during this phase; hence the classiflcation "continuum + 
emission" objects. All such objects drive energetic winds, some of which 
are manifest as highly collimated stellar jets (Strom et al. 1988; Cabrit et 
al. 1989). 

• The first appearance of the stellar photosphere, as the contribution 
of the disk to the YSO luminosity decreases {T Tauri or TTS (0.2 < Af/M© 
Tauri < 1/5) and Herbig emission star or HES (1.5 < MIMq < 5) phase). 
Relatively massive disks are still present, but the accretion rate and mass 
outflow rate both diminish. The infrared luminosity from accretion and the 
boundary layer emission decrease as a consequence of the reduced accretion 
rate through the disk. "Reprocessing" of steUar radiation absorbed by dust 
in the accretion disk and re-radiated in the infrared contributes up to 0.5 
times the steUar luminosity (depending on the inclination of the star/disk 
system with respect to the line of sight). The observed infrared spectra show 
the combined contribution from a Rayleigh-Jeans (AFa ~ A~^) component 
from the stellar photosphere and a broader, less rapidly falling (A~^/^ to 
A~'*/^) component arising from both disk accretion and passive reprocessing 
by circumstellar dust (Figure 2). Photospheric absorption spectra are visible, 
though sometimes partiaUy "veUed" by the hot boundary layer emission. H 
emission is strong (typical equivalent widths ranging from 10 < W^ < 100 
A). In TTS, Ca II and selected forbidden and pace permitted metallic Unes 
are often prominent in emission. Energetic winds persist, although their 
morphology and interaction with the circumstellar environment is unknown 
at this stage. Highly collimated optical jets are not seen, but spatially 
unresolved [O I] Une profile structures require that the winds be at least 
moderately collimated (on scales of ~ 100 AU). 

• The settling of dust into the midplane of the disk followed by 
the clearing of distributed material in the disk, as dust agglomerates into 
planetesimals, first in the inner regions of the disk where terrestrial planets 
form, and later in the outer disk where giant planets and comets are 







E -10 

T i j 1 1 1 1 1~ 

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1 L_ 1 l__i _l_ „i I I I _L ] L l-_ I _ -1 i— 1 - J 1 I 1 - 1- 

4.5 -4 -3.5 -3 


X (cm) 

FIGURE 2 A plot of the reddening-corrected spectral energy distribution (0.35/i < A < 
100 /i) for the T Tauri star, FX Tku (open circles). Also plotted is the spectral energy 
distribution of a dwarf standard star (filled triangles) of spectral type Ml V corresponding 
to that of FX TSu. The flux of the TTS and the standard star have been forced to agree 
at R (0.65/z). 

assembled. The disappearance of accretion signatures and energetic winds 
{"naked" T Tauri or NTTS phase?). 

• The appearance of the star on the hydrogen-burning main se- 
quence, accompanied by its planetary system and possibly by a tenuous 
remnant or secondary dust disk (analogous to the edge-on disk surround- 
ing B. Pictoris imaged recently by Smith and Tferrile 1984). 

Is this picture correct even in broad outline for all single stars? Are 
disks formed around members of binary and multiple star systems (which 
constitute at least 50% of the stellar population in the solar neighborhood)? 
For those stars that form disks, what is the range of disk sizes and masses? 
What is the range in time scales for disk evolution in the inner and outer 
disks, and how do these time scales compare with those inferred for our 
solar system from meteoritic and primitive body studies, and theoretical 
modeling of the early solar nebula? In what fraction of star/disk systems 
can the gas in the outer disk regions survive removal by energetic winds 
long enough to be assembled into analogs of the giant planets? 


Current Observational Evidence Tor Disks 
Associated with Pre-Main Sequence Stars 

Observations carried out over the past five years provide strong evi- 
dence for circumstellar disks associated with many young stars (ages < 3 x 
10® years) of a wide range of masses. These disks appear to be massive (M 
~ 0.01 to 0.1 Mq) precursor structures to the highly evolved, low-mass (M 
~ 10"''^ M©)) disks discovered recently around B-Pictoris and its analogs 
(Smith and Tbrrile 1984; Backman and Gillett 1988): 

• The direct and speckle imaging at near-infrared wavelengths (Gras- 
dalen et al. 1984; Beckwith et al. 1984; Strom et al. 1985) reveal flattened, 
disk-like structures associated with three YSOs: HL Tku (a low-mass con- 
tinuum -»■ emission star), R Mon (an intermediate-mass continuum + 
emission star), and L1551/IRS 5 (a k)w-mass embedded infrared source). 
These structures are seen via light scattered in our direction by sub-micron 
and micron-size dust grains. Associated structures are also seen in mm- 
continuum and CO line images obtained with the Owens \^lley interferom- 
eter (Sargent and Beckwith 1987), although the relationship between the 
optical and near-infrared and mm-region structures is not clear at this point. 
Shu (1987, private communication) has argued that the flattened, scattered 
light structures detected to date trace not disks, but rather remnants of 
infalling, protostellar cores (see also Grasdalen et al. 1989). 

• llie high-spectral resolution observations of [O I] and [S II] lines in 
continuum + emission, T Ikuri, and Herbig emission stars provide indirect 
but compeUing evidence of such disks. Hie forbidden line emission is 
associated with the outer (r ~ 10 to 100 AU) regions of winds driven by 
PMS stars. However, in nearly aU cases studied to date, only blue-shifted 
emission is observed (see Figure 3) thus requiring the presence of structures 
whose opacity and dimension is suflicient to obscure the receding part of 
the outflowing gas diagnosed by the forbidden lines (Edwards et aL 1987; 
Appenzeller et al. 1984). 

• The broad, far-infrared (A > lO/i) spectra charaaeristic of all 
rantinuum + emission, T Tkuri, and Herbig emission stars arise from 
heated dust located over a wide range of distances (~ 0.1 to > 100 AU) 
from a central pre-main sequence (PMS) star (RucinsW 1985; Rydgren 
and Zak 1986). In order to account for the fact that these IR-luminous 
YSOs are visible at optical wavelengths, it is necessary to assume that the 
observed far-IR radiation arises in an optically thick but physically thin 
circumstellar envelope: a disk. If the heated circumstellar dust responsible 
for the observed far-infrared radiation intercepted a large solid angle, the 


i-5 I I I I I T T 1 I I I I I I I 1 I I I I I I I t I I I t I I I I I I 1 I I t t t I I I I I I I I I I 






1 1 , , 

, , 1 , 

i_i Lj 


V (km/sec) 






FIGURE 3 A plot of the [0 I] A 6300 A profile observed for the T Thuii star, CW Tiu. 
Note the broad, double-peaked profile extending to blue-shifted (negative) velocities; there 
is no corresponding red-shifted emission. The [0 I] emission is believed to trace low density, 
outflowing gas located at distances r > 10 AU from the surface of CW "Bu. The absence 
of red-shifted emission is attributed to the presence of an opaque circumstellar disk whose 
size is comparable to or larger than the region in which [0 I] emission is produced. 

associated PMS stars could not be seen optically (Myers et al. 1987; Adams 
et al. 1987). The observed far-IR fluxes require a mass of emitting dust 
10-^ to 10-'' Mo or a total disk mass of 0.1 to 0.01 M© (assuming a 
gas/dust ratio appropriate to the interstellar medium). 

• The optical and infrared spectra of a class of photometrically 
eruptive YSOs known as FU Ori objects appear to arise in self-luminous, 
viscous accretion disks characterized by a temperature-radius relation of 
the form T ~ r"^/^ (Hartmann and Kenyon 1987a,b; Lynden-Bell and 
Pringle 1974). Because material in this disk must be in Keplerian motion 
about a central PMS star, absorption lines formed in the disk reflect the 
local rotational velocity. High spectral resolution observations show that 
lines formed in the outer, cooler regions of the disk are narrower than 
absorption features formed in the inner, hotter, more rapidly rotating disk 
regions (Hartmann and Kenyon 1987a,b; Welty et al. 1989), thus providing 


important kinematic confirmation of disk structures associated with PMS 

• The mm-line and continuum observations of HL Tiiu and L1551/ 
IRS 5 made with the OVRO mm interferometer suggest that circumstellar 
gas and dust is bound to the central PMS star and, in the case of HL Tliu, 
in Keplerian motion about the central object (Beckwith and Sargent 1987). 

IVequency of Disk Occurrence 

What fraction of stars are surrounded by disks of distributed gas and 
dust at birth? If excess infrared and mm-wave continuum emission is 
produced by heated dust in disks, then all continuum + emission, T Tkuri, 
and Herbig emission stars must be surrounded by disks. The inferred 
disk masses (0.01 < Md.-ji/Mo < 0.1, comparable to the expected mass of 
the primitive solar nebula) and optical depths (ry ~ 1000) for TTS and 
HES are relatively large (Beckwith et al. 1989 and Edwards et al. 1987 for 
estimates based on mm-continuum and far-IR measurements respectively). 

However, the HR diagram presented by Wilter et al. (1988) suggests 
that ~ 50% of low mass pre-main sequence stars with ages comparable to 
those characterizing TTS (t < 3 x 10® years) are "naked" T Tkuri stars 
(NTTS) which lack measureable infrared emission, and therefore massive, 
optically thick disks. The observations of \%mer et al. (1977) suggest that 
a comparable percentage (50% to 70%) of young (t < 3 x 10® years) 
intermediate mass stars (M ~ 1.5-2.0 M©) also lack infrared excesses. 

Recently, Strom et al. (1989) examined the frequency distribution of 
near-IR (12/i) excesses, AK = log {¥2.7^ (PMS star)/ F2.2P (standard 
star)}, associated with 47 NTTS and 36 TTS in Tkurus-Auriga (see Figure 
4). They find that 84% of the TTS and 36% of the NTTS have significant 
excesses, AK > 0.10 dex. Thus, nearly 60% of solar-type PMS stars with 
ages t < 3 X 10® years located in this nearby star-forming complex have 
measurable^ infrared excesses; these excesses most plausibly arise in disks. 
However, the sample includes only known PMS stars for which adequate 
photometry is available; more NTTS may yet be discovered when more 
complete x-ray and proper motion searches of the Tkurus-Auriga clouds 
become available. It is also important to note that these disk frequency 
statistics exclude several PMS stars which show small or undetectable near 
IR excesses, but relatively strong mid- to far-IR excesses (see Figure 5): 

Objects that lack measurable infrared excessescoulcf^ surrounded by low mass, tenuous 
disks (M <C 10~ M0)disks. Fbrexample,adiskofmasscomparabletothatsurroundlng/?Pic 
(M ~ 10~ Mq) could not be detected around a PMS star in the 'burus- Auriga clouds given 
the current sensitivity of IR measurements. 





1 — I — I — I I r 

n — I — I — m — I — ] — I — I — 1 I I 1 i I i I r 

Distribution of AK for NTTS 

I I I I I I 

A I ,1... 



I I I 1 I I 1 I I I I 1- 


1 1.2 



Z 10 

n — 1 — I — I — I — 1 — I i I r 

I I I I 1 — L. 

n — I — I — I — t — I — 1 — I — I — r 

Distribution of AK for TTS 

J I I I I — u 

.4 .6 




FIGURE 4 The frequency distribution of the Z.2fl excess, AK = log {F2.2;i (PMS)/F2.2;i 
(standard)}, for NTTS (top) and TTS (bottom). Note that a) 36% of the NTTS show 
excesses, AK > 0.10 dex, and b) that while the distribution for the NTTS peaks toward 
smaller values of AK, there is significant overlap in the two distribution. It does not appear 
as if NTTS as a class lack infrared excesses. 


these objects may represent PMS stars surrounded by circumstellar disks 
which are optically thin near the star (and therefore produce too little 
near-IR radiation to be detected), but optically thick at distances r > 1 AU 
(see below). 

Do pre-main sequence stars with ages t < 3 x 10^ years that lack 
infrared excesses (40% of all solar-type PMS stars) represent a population 
of stars bom without disks? Or have their disks been destroyed by tides 
raised by a companion star? Or have some fraction of these young PMS 
stars already built planetary systems? 

The Effect of Stellar Companions on Disk Survival 

Do disks form around members of binary and multiple star systems? 
If so, are these disks perturbed by tidal forces and perhaps disrupted when 
the disk size is comparable to the separation between stellar components? 
lb date, the overwhelming majority of binaries discovered among low- and 
intermediate-mass PMS stars in nearby star-forming complexes have been 
wide (A^ > 1"; r > 150 AU) doubles with separations well in excess of the 
radius of our solar system (and thus possibly of lesser interest to addressing 
the above questions). In the last few years, ground-based observations 
have uncovered a few examples of a) spectroscopic binaries with velocity 
amplitudes, Av > 10 km/s (separations < 3 AU; Hartmann et al. 1986); b) 
binaries with separations in the range 0.1 to 50 AU detected from lunar 
occultation observations of YSOs in Tiiurus-Auriga and Ophiuchus (Simon, 
private communication); and c) binaries discovered in the course of optical 
and infrared speckle interferometric observations (Chelli et al. 1988). Of 
the known binaries in Tkurus-Auriga with observed or inferred separations 
A^ < 0.5" (r < 70 AU; DF "Ru, FF T&u, HV T^u, HQ Tku, T Tku), all 
but FF Tku appear to have IR excesses similar to those of TTS thought 
to be surrounded by disks. This somewhat surprising result implies that 
circumstellar envelopes of mass > lO"** M© and of dimension 10 to 100 
AU are present even in close binary systems. 

Disk Evolutionary Time Scales 

On what time scales do disks evolve from massive "primitive" to low 
mass, perhaps "post planet-building" disks? Current observations suggest 
that more than 50% of low- to intermediate-mass PMS stars with ages t < 
3 X 10® years are surrounded by disks with masses in excess of 0.01 M0 of 
distributed material (see above). There are no known main sequence stars 
surrounded by this much distributed matter, although a few stars such as 
Vega and /? Pictoris (Smith and Tferrile 1984; Backman and Gillett 1988) 

I ' ' ' ' I ' I ' ' I ' ' ' ' I ' ' ' ' I 



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J. (cm) 


FIGURE 5 A plot of the reddening-corrected spectral energy distributions (0.35/i < A < 
100/i) for 7 NTTS and the T Thuri star, FX "Bu (see Figure 2); the observed points 
for the NTTS and ITS are plotted as open circles. Also plotted are the spectral energy 
distributions of dwarf standard stars (filled triangles) of spectral types corresponding to 
those of the NTTS and TTS. The fluxes of the NTTS and those of the standard stars have 
been forced to agree at R (0.65/i). Note the small near-infrared excess and relatively lai^e 
mid- to lar-infrared excesses for several of the NTTS. A spectral eneigy distribution of this 
character might be produced by a circumslellar disk in which the optical depth of emitting 
material in the Inner disk is small, while that in the outer disk is large. 


are surrounded by disks with masses ~ 10"'^ M© (~ 0.1 Earth masses). 
Thus, disks surrounding newborn stars must evolve to a more tenuous state. 

Recent work by Strom et at. (1989) suggests that nearly 60% of PMS 
stars in TSurus-Auriga with ages younger than 3 x 10® years, and only 40% 
of older stars, show evidence of significant near-infrared excesses AK > 
0.1 dex (see above). These results are illustrated in Figure 6. Fewer than 
10% of PMS stars older than 10'^ years show AK > 0.1. If excess near-IR 
emission arises in the warm, inner regions of circumstellar disks, then we 
can use these statistics to discuss the range of time scales for disks to evolve 
from massive, optically thick structures (with large K values) to low-mass, 
tenuous entities (with small AK values). 

If all solar-type stars form massive (0.01 to 0.1 M© disks, then by t = 
3 X l(f years, 40% of PMS stars (the fraction of young PMS stars with 
AK < 0.10) are surrounded by remnant disks too tenuous to detect. The 
evolutionary time scale for such rapidly evolving disks must be t <C 3 x 10® 
years. Because fewer than 10% of PMS stars older than 10^ years show AK 
> 0.1 (Strom et al. 1989), the disks surrounding all but 10% of PMS stars 
must have completed their evolution by this time. The majority of disks 
must have evolutionary time scales in the range 3 x 10® to 10^ years. This 
range represents the best astrophysical constraint on the Ukely time scale 
for planet building available at present. 

As noted earlier, the above statistics obtain for all known TTS and 
NTTS in Tiurus-Auriga for which adequate photometry is available. Al- 
though the exact fraction of PMS stars surrounded by disks may change 
somewhat as more complete surveys for PMS stars become available, our 
qualitative conclusions regarding the approximate time scale range for disk 
evolution are unlikely to be vitiated. 

Disk Sizes and Morphologies 

In our solar system, all known planets lie within 40 AU of the Sun. 
Yet the circumstellar disk imaged around Pic extends to a distance 
approximately several thousand AU from the central star. Do primitive 
solar nebulae typically extend to radii considerably larger than our own 
planetary system? If so, how far, and how much material do they contain? 
How do properties such as size and surface mass distribution change with 
time? Do such changes reflect the consequences of angular momentum 
transport within the disk? Of planet building episodes? 

Current estimates of disk sizes are indirect, and are based on: (1) the 
size of the YSO wind region required to account for the observed blue- 
shifted [O I] and [S II] forbidden line emission fluxes; disks must be large 
enough to occult the receding portion of the stellar wind (Appenzeller et al. 
1984; Edwards et al. 1987) and (2) the projected radiating area required to 







\ ■ ' • i 

Distribution of aK for NTTS 


FIGURE 6 The frequency distribution of the near-infrared excess AK (see text) for stats 
with ages t > 3 X 10^ yeare and t < 3 X 10® years. Note that a) nearly 60% of young 
PMS stars have measurable (AK > 0.10) near-infrared excesses and b) that the fraction of 
PMS stars with such excesses decreases for ages t > 3 X 10® years. If IR excesses derive 
from emitting dust embedded in massive, optically thick circumstellar disks surrounding 
PMS stars, then the fraction of stars surrounded by such disks must decrease with time. 
Our data suggests that the time scales for evolving from a massive, optically thick disk to 
a low mass, tenuous disk must range from ~ 3 X 10® to 10^ yeais. This range represents 
the best available astrophysical constraint on the time scale for planet building. 

explain the observed far-infrared radiation emanating from optically thick, 
cool dust in the outer disk regions (Myers et al. 1987; Adams et al. 1987). 
In both cases, these estimates provide lower limits to the true extent of the 
disk. Edwards et al. (1987) have shown that these independent methods 
predict comparable lower limit disk size estimates: r<j,-,jt > 10 to 100 AU, 
for a sample of continuum + emission, T Thuri, and Herbig emission stars. 
At the distance of the nearest star-forming regions, such disks intercept 
an angular radius, r > 0.07 to 0.7 arc seconds. Thus far, it has proven 
difficult to image disks of this size from the ground. Decisive information 
regarding disk isophotal sizes and surface brightnesses must await sensitive 


imaging with HST, whose stable point spread function and high angular 
resolution will permit imaging of low-surface brightness circumstellar disks 
around bright PMS stars. When available, HST measurements of disk 
sizes will prove an invaluable complement to ground-based sub-mm and 
mm-continuum measurements which provide strong constraints on the disk 
mass, but which lack the spatial resolution to determine size. Tbgether, these 
data will yield average surface mass densities and estimates of midplane 
optical depths — critical parameters for modeling the evolution of primitive 
solar nebulae. 

Prior to HST, ground-based observations of the ratio of near- to far- 
IR excess radiation may provide a qualitative indication of the distribution 
of material in circumstellar disks. For example, Strom et al. (1989) discuss 
several solar-type PMS stars which show small near-IR excesses compared 
to far-IR excesses (Figure 5). They suggest that the disks surrounding 
these stars have developed central holes as a first step in their evolution 
from massive, optically thick structures (such as those surrounding TTS) 
to tenuous structures (such as those surrounding /? Pic and Vega). Such 
central holes may provide the first observational evidence of planet-building 
around young stars. 

The Disk Environment 

High resolution ground-based spectra suggest that energetic winds 
(Luiind > 0.01 L,; V ~ 200 kilometers per second) characterize all TTS 
and HES (Edwards and Strom 1988). However, mass-loss rates are not 
well determined: estimates range from 10~® to 10~^ M© per year and are 
greatly hampered by uncertainties in our knowledge of the wind geometry. 
The broad, blueshifted, often double-peaked forbidden line profiles of [O 
I] and [S II] (see Figure 3), suggest that typical TTS and HES winds 
are not spherically symmetric and may be at least moderately collimated. 
The modek proposed to account for the forbidden line profiles include 
a) latitude-dependent winds characterized by higher velocities and lower 
densities in the polar regions, b) sub-arc second, highly coUimated polar 
jets; and c) largely equatorial mass outflows obliquely shocking gas located 
at the raised surface of a slightly flaring disk (Hartmann and Raymond 

Knowledge of the wind geometry is necessary if we are to derive 
more accurate estimates of PMS star mass loss rates from [O I] profiles. 
Depending on their mass loss rate and geometry, PMS star winds may have 
a profound effect on the survival of gas in circumstellar disks and on the 
physical and chemical characteristics of the grains: 


• Energetic winds can remove gas from the disk during the epoch 
of planet building, thereby eliminating an essential "raw material" for 
assembling massive giant planets in the outer disk. 

• Exposure of interstellar grains to ~ 1 kev wind particles carried 
by a wind with M ~ 10"^ M© per year for times of 10^ to lO'' years, 
can alter the chemical composition of grain mantles. For a grain with a 
water-ammonia-methane-ice mantle, energetic particle irradiation can in 
principle: (1) create large quantities of complex organic compounds on 
grain surface and (2) drastically reduce the grain albedo (Greenberg 1982; 
Lanzerotti et al. 1985; Strazzula 1985). Recent observations of the dust 
released from the nucleus of comet Halley show these grains to be "black" 
(albedos of ~ 0.02 to 0.05) and probably rich in organic material (Chyba 
and Sagan 1987). Does this cometary dust owe its origin to irradiation of 
grains by the Sun's T T^uri wind during the early lifetime of the primitive 
solar nebula? 

HST will allow us to image low-density, outflowing ionized gas in the 
light of [O I] A6300 A and thus allow us to trace YSO wind morphologies 
directly. HST observations will determine whether energetic outflows in- 
teract with the disk (as opposed to leaving the system in highly collimated 
polar jets). In combination with improved estimates of mass outflow rates, 
we can then determine the integrated flux of energetic particles through the 
disk for a sample of PMS objects of differing age and thus assess the role 
of winds in the evolution of disks. 


The authors acknowledge support from the National Science Founda- 
tion, the NASA Asuophysics Data Program (IRAS and Einstein), and the 
NASA Planetary Program. Many of the arguments developed here have 
been sharpened and improved following consultation with Steven Beckwith, 
Robert A Brown, Belva CampbeU, Luis Carrasco, H. Melvin Dyck, Gary 
Grasdalen, Lee Hartmann, S. Eric Persson, Frank Shu, T. Simon, M. Simon, 
R. Stachnik, John Stauffer, and Fred Vrba. Comments from Sylvie Cabrit, 
Scott Kenyon and Michael Skrutskie have also been valuable. 


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the Fifth Cambridge Cool Star Workshop. Springer, Verlag. 
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Numerical Two-Dimensional Calculations 
of the Formation of the Solar Nebula 

Peter H. Bodenheimer 
Lick Observatory 


The protostellar phase of stellar evolution is of considerable impor- 
tance with regard to the formation of planetary systems. The initial mass 
distribution and angular momentum distribution in the core of a molecular 
cloud determine whether a binary system or a single star is formed. A rel- 
atively slowly rotating and centrally condensed cloud is likely to collapse to 
a disk-like structure out of which planets can form. The above parameters 
then determine the temperature and density structure of the disk and the 
characteristics of the resulting planetary system. 

There has been considerable recent interest in two-dimensional nu- 
merical hydrodynamical calculations with radiative transfer, applied to the 
inner regions of collapsing, rotating protostellar clouds of about 1 Mq. 
The calculations start at a density that is high enough so that the gas 
is decoupled from the magnetic field. During the collapse, mechanisms 
for angular momentum transport are too slow to be effective, so that an 
axisymmetric approximation is sufficiently accurate to give useful results. 
Until the disk has formed, the calculations can be performed under the 
assumption of conservation of angular momentum of each mass element. 
In a numerical calculation, a detailed study of the region of disk formation 
can be performed only if the central protostar is left unresolved. 

Wiih a suitable choice of initial angular momentum, the size of the 
disk is similar to that of our planetary system. The disk forms as a relatively 
thick, warm equilibrium structure, with a shock wave separating it from the 
surrounding infalling gas. The calculations give temperature and density 



distributions throughout the infalling cloud as a function of time. From 
these, frequency-dependent radiative transfer calculations produce infrared 
spectra and isophote maps at selected viewing angles. The theoretical spec- 
tra may be compared with observations of suspected protostellar sources. 
These disks correspond to the initial conditions for the solar nebula, whose 
evolution is then driven by processes that transport angular momentum. 


From observations of physical and cosmochemical properties of the 
solar system and from astronomical observations of star-forming regions 
and young stars, certain constraints can be placed on the processes of 
formation and evolution of the solar nebula. 

a) Low-mass stars form by the collapse of initially cold (10 K), 
dense (10^ particles cm"^) cores of molecular clouds. The close physical 
proximity of such cores with T Tkuri stars, with imbedded infrared sources 
which presumably are protostars, and with sources with bipolar outflows, 
presumably coming from stars in a very early stage of their evolution, lends 
support to this hypothesis (Myers 1987). 

b) The specific angular momenta (j) of the cores, where observed, 
fall in the range 10^° - 10^^ cm' s-^ (Goldsmith and Arquilla 1985; 
Heyer 1988). In the lower end of this range, the angular momenta are 
consistent with the properties of our solar system: for example, Jupiter's 
orbital motion has j s» 10^° cm' 8"^ In the upper end of the range, 
collapse with conservation of angular momentum would lead to a halt of 
the collapse as a consequence of rotational effects at a characteristic size 
of ~ 2000 AU, far too large to account for the planetary orbits. In fact, 
hydrodynamical calculations suggest that collapse in this case would in fact 
lead to fragmentation into a binary or multiple system. 

c) The infrared radiation detected in young stars indicates the pres- 
ence of disks around these objects (Hartmann and Kenyon 1988). A 
particularly good example, where orbital motions have been observed, is 
HL Tku (Sargent and Beckwith 1987). The deduced masses of the disk and 
star are 0.1 Mq and 1.0 M©, respectively. The radius of the disk is about 
2000 AU. Roughly half of all young pre-main-sequence stars are deduced 
to have disks, mostfy unresolved, with masses in the range 0.01-0.1 Mq and 
sizes from 10 to 100 AU (Strom et aL 1989). 

d) The rotational velocities of T Tkuri stars are small, typically 20 km 
S-* or less (Hartmann et aL 1986). The distribution of angular momentum 
in the system consisting of such a star and disk is quite different from 
that in the core of a molecular cloud, which is generally assumed to be 


uniformly rotating witli a power-law density distribution. Substantial angular 
momentum transport, from the central regions to the outer regions, must 
take place early in the evolution. The required transport is unlikely to 
occur during collapse; therefore it must occur during the disk evolution 
phase before the star emerges as a visible object. 

e) The lifetime of the pre-main-sequence disks is difficult to deter- 
mine from observation, but it probably does not exceed 10^ years (Strom 
et al. 1989). The mechanisms for angular momentum transport, which 
deplete disk mass by allowing it to fall into the star, must have time scales 
consistent with these observations, as well as with time scales necessary to 
form gaseous giant planets. 

f) The temperature conditions in the early solar nebula can be 
roughly estimated from the distribution of the planets' and satellites' mass 
and chemical composition (Lewis 1974). The general requirements are that 
the temperature be high enough in the inner regions to vaporize most solid 
material, and that it be low enough at the orbit of Jupiter and beyond to 
allow the condensation of ices. Theoretical models of viscous disks produce 
the correct temperature range, as do collapse models of disk formation with 
shock heating. 

g) The evidence from meteorites is difficult to interpret in terms 
of standard nebular models. First, there is evidence for the presence of 
magnetic fields, and second, the condensates indicate the occurrence of 
rapid and substantial thermal fluctuations. Suggestions for explaining this 
latter effect include turbulent transport of material and non-axisymmetric 
structure (density waves) in the disk. 

h) The classical argument, of course, is that the coplanarity and 
circularity of the planets' orbits imply that they were produced in a disk. 

i) A large fraction of stars are observed to be In binary and mul- 
tiple systems (Abt 1983); the orbital values of j in the closer systems are 
comparable to those in our planetary system. It has been suggested (Boss 
1987; Safronov and Ruzmaikina 19«5) that if the initial cloud is slowly 
rotating and cenfrally condensed, it is likely to form a single star rather 
than a binary. Pringle (1989) has pointed out that if a star begins collapse 
after having undergone slow diffusion across the magnetic Held, it will be 
centrally condensed and will therefore form a single star. If, however, the 
collapse is induced by external pressure disturbances, the outcome is likely 
to be a binary. On the other hand, Miyama (1989) suggests that single star 
formation occurs in initial clouds with j « 10^' cm^ s~^ After reaching a 
rotationally supported equilibrium that is stable to fragmentation, the cloud 
becomes unstable to nonaxisymmetric perturbations, resulting in angular 
momentum transport and collapse of the central regions. 



The above considerations illustrate several of the important questions 
relating to the formation of the solar nebula: What are the initial conditions 
for collapse of a protostar? At what density does the magnetic field 
decouple from the gas? What conditions lead to the formation of a single 
star with a disk rather than a double star? Can the embedded IRAS sources 
be identified with the stage of evolution just after disk formation? What is 
the dominant mechanism for angular momentum transport that produces 
the present distribution of angular momentum in the solar system? The 
goal of numerical calculations is to investigate these questions by tracing 
the evolution of a protostar from its initial state as an ammonia core in a 
molecular cloud to the final quasi-equiUbrium state of a central star, which is 
supported against gravity by the pressure gradient, and a circumstellar disk, 
which is supported in the radial direction primarily by centrifugal effects. 
A further goal is to predict the observational properties of the system at 
various times during the collapse. A full treatment would include a large 
number of physical effects: the hydrodynamics, in three space dimensions, 
of a collapsing rotating cloud with a magnetic field; the equation of state of 
a dissociating and ionizing gas of solar composition, cooling from molecules 
and grains in optically thin regions; frequency-dependent radiative transfer 
in optically thick regions; molecular chemistry; the generation of turbulent 
motions as the disk and star approach hydrostatic equilibrium; and the 
properties of the radiating accretion shock which forms at the edge of the 
central star and on the surfaces of the disk (Shu et al. 1987). 

The complexity of this problem makes a general solution intractable 
even on the fastest available computing machinery. For example, the length 
scales range from 10^'' centimeters, the typical dimension of the core of 
a molecular cloud, to 10" centimeters, the size of the central star. The 
density of the material that reaches the star undergoes an increase of about 
15 orders of magnitude from its original value of ~10~*^ g cm~^. Also, 
the numerical treatment of the shock front must be done very carefully. 
The number of grid points required to resolve the entire structure is veiy 
large in two space dimensions; in three dimensions it is prohibitively large. 
Even if the detailed structure of the central object is neglected and the 
system is resolved down to a scale of 0.1 AU, the Courant-Friedrichs- 
Lewy condition in an explicit calculation requires that the time step be 
less than one-millionth of the collapse time of the cloud. Therefore, 
a number of physical approximations and restrictions have been made 
in all recent numerical cakulations of nebular formation. For example, 
magnetic fields have not been included, on the grounds that the collapse 
starts only when the gas has become almost completely decoupled from 
the field because of the negligible degree of ionization at the relatively 


high densities and cold temperatures involved. Also, in most calculations, 
turbulence has been neglected during the collapse. Even if it is present, the 
time scale for transport of angular momentum by this process is expected 
to be much longer than the dynamical time. It turns out that angular 
momentum transport can be neglected during the collapse, and therefore 
an axisymmetric (two-dimensional) approximation is adequate during this 
phase. Three-dimensional effects, such as angular momentum transport by 
gravitational torques become important later, during the phase of nebular 
evolution. A further approximation involves isolating and resolving only 
specific regions of the protostar. In one-dimensional calculations (Stahler 
et al. 1980), it has been possible to resolve the high-density core as well 
as the low-density envelope of the protostar. However, in two space 
dimensions, proper resolution of the region where the nebular disk forms 
caimot be accomplished simultanously with the resolution of the central 
star. In several calculations the outer regions of the protostar are also not 
included, so the best possible resolution can be obtained on the length scale 
1-50 AU. Thus the goal outlined above, the calculation of the evolution of 
a rotating protostar all the way to its final stellar state, has not yet been 
fully realized. 

The stages of evolution of a slowly rotating protostar of about 1 M© 
can be outlined as follows: 

a) The frozen-in magnetic field transfers much of the angular mo- 
mentum out of the core of the molecular cloud, on a time scale of lO'^ 

b) TTie gradual decoupling between the magnetic field and the matter 
allows the gas to begin to collapse, with conservation of angular momentum. 

c) The initial configuration is centrally condensed. During collapse, 
the outer regions, with densities less than about 10~'^ g cm"^ remain 
optically thin and collapse isothermally at 10 K. The gas that reaches 
higher densities becomes optically thick, most of the released energy is 
trapped, and heating occurs. 

d) The dust grains, which provide most of the opacity in the pro- 
tostellar envekspe, evaporate when the temperature exceeds 1500 K An 
optically thin region is created interior to about 1 AU. Further, at temper- 
atures above 2000 K, the molecular hydrogen dissociates, causing renewed 
instability to collapse. 

e) The stellar core and disk form from the inner part of the cloud. 
The remaining infalling material passes though accretion shocks at the 
boundaries of the core and disk; most of the infall kinetic energy is con- 
verted into radiation behind the shock. The surrounding infalling material 
is optically thick, and the object radiates in the infrared, with a peak at 
around 6()-100 /im. 


f) A Stellar wind is generated in the stellar core, by a process that 
is not well understood. The wind breaks through the infalling gas at the 
rotational poles, where the density gradient is steepest and where most of 
the material has afready fallen onto the core. This bipolar outflow phase 
lasts about 10" years. 

g) Infall stops because of the effects of the wind, or simply because 
the material is exhausted. The stellar core emerges onto the Hertzspning- 
Russell diagram as a T Tburi star, still with considerable infrared radiation 
coming from the disk. 

h) The disk evoh'es, driven by processes that transfer angular momen- 
tum, on a timescale of 10^ to 10^ years. Angular momentum is transferred 
outwards through the disk while mass is transferred inwards. The rotation 
of the central object slows, possibly through magnetic braking in the stellar 
wind. Possible transport processes in the disk include turbulent (convec- 
tively driven) viscosity, magnetic fields, and gravitational torques driven by 
gravitational instability in the disk or by non-axisym metric instabilities in 
the initially rapidly rotating central star. 

The following sections describe numerical calculations of phases b 
through e, from the time when magnetic effects become unimportant to the 
time when at least part of the infalling material is approaching equilibrium 
in a disk. 


Modern theoretical work on this problem goes back to the work of 
Cameron (1962, 1963), who discussed in an approximate way the collapse 
of a protostar to form a disk. In a later work, Cameron (1978) solved 
numerically the one-dimensional (radial) equations for the growth of a 
viscous accretion disk, taking into account the accretion of mass from an 
infalling protostellar cloud. The initial cloud was assumed to be uniformly 
rotating with uniform density. The hydrodynamics of the inflow was not 
calculated in detail; rather, infalling matter was assumed to join the disk 
at the location where its angular momentum matched that of the disk. A 
similar approach was taken by Cassen and Summers (1983) and Ruzmaikina 
and Maeva (1986), who, however, took into account the drag caused by 
the infalling material, which has angular momentum different from that 
of the disk at the arrival point. The latter authors discuss the turbulence 
that devetops for the same reason (see also Safronov and Ruzmaikina 
1985). This section concentrates on full two-dimensional calculations of the 
collapsing cloud during the initial formation of the disk. 

One approach to this problem (Tkharnuter 1981; Regev and Shaviv 
1981; Morfill et al. 1985; Ticharnuter 1987) is based on the assumption that 


turbulent viscosity operates during the collapse. The resulting transport of 
angular momentum out of the inner parts of the cloud might be expected 
to suppress the fragmentation into a binary system and to reduce the 
angular momentum of the central star to the point where it is consistent 
with observations of T Tkuri stars. The procedure is to assume a simple 
kinematic viscosity u = 0.33 ac.L, where c, is the sound speed, L is 
the length scale of the largest turbulent eddies, and a is a free parameter. 
Subsonic turbulence is generally assumed, so that a is less than unity. Once 
the collapse is well underway, the sound crossing time is much longer than 
the free fall time, so that angular momentum transport is actually relatively 
ineffective. Binary formation is probably suppressed, but the material that 
falls into the central object still has high angular momentum compared with 
that of a T Tiiuri star. 

Nevertheless, the model presented by MorfiU et al. (1985) provides 
interesting information regarding the initial solar nebula. In contrast to the 
earlier calculation of Regev and Shaviv (1981), which used the isothermal 
approximation, this two-dimensional numerical calculation included the 
full hydrodynamical equations, applicable in both the optically thin and 
optically thick regions. Radiation transport was included in the Eddington 
approximation. The calculations started with 3 M© at a uniform density of 
10~2° g cm~^ and with uniform angular velocity. TWo different values for j 
were tested, 10^' and 10^° cm^ s'S with qualitatively similar results. The 
case with lower angular momentum is the one of most interest. The collapse 
proceeds and results in the formation of a central condensation surrounded 
by a disk. However, the core does not reach hydrostatic equilibrium but 
exhibits a series of dynamical oscillations, driven, according to the authors, 
by heat generated through viscous dissipation in the region near the edge of 
the core. The dynamical expansion is accompanied by an outgoing thermal 

So that the development of the disk could be studied, the computa- 
tional procedure was modified to treat the region interior to 2 x 10'^ cm 
as an unresolved core, and thereby to suppress the oscillations. Matter and 
angular momentum were allowed to flow into this central region but not 
out of it The kinetic energy of infall was assumed to be converted into 
radiation at the same boundary. The calculation was continued until about 
0.5 M© had accumulated in the core, and about 0.1 M© had collapsed into 
a nearly Keplerian disk, with radial extent of about 20 AU. The calculation 
was stopped at that point because of insufficient spatial resolution in the 
disk region, and because the ratio (13) of rotational kinetic energy to gravi- 
tational potential energy of the core exceeded 0.27, so dynamical instability 
to non-axisymmetrlc perturbations would be likely (Durisen and Tbhline 
1985). The development of a triajdal central object is Ukely to result in the 
transport of angular momentum by gravitational torques (Yuan and Cassen 


1985; Durisen et al. 1986). Angular momentum would be transported from 
the central object to the disk, and the value of p for the core would be 
reduced below the critical value. However, its remaining total angular 
momentum would be still too large to allow it to become a normal star. 

A further important feature of the calculation was its prediction of the 
temperatures that would be generated in the planet-forming region. Over 
a time scale of 3 x 10^ years the temperature of material with the same 
specific angular momentum as that of the orbit of Mercury ranged from 
400-600 K The predicted temperature for Jupiter remained fairly constant 
at 100 K, while that for Pluto approximated 15 K In the inner region of the 
nebula these temperatures are slightly cooler than those generally thought 
to exist during planetary formation or those calculated in evolving models 
of a viscous solar nebula (Ruden and Lin 1986). 

A further calculation was made by TScharnuter (1987) with similar 
physics but a different initial condition. A somewhat centrally condensed 
and non-spherical cloud of 1.2 M© starts collapse from a radius of 4 x 10'^ 
cm, a mean density of 8 x 10~^^ g cm~^, and j w 10^° cm^ s~^ A major 
improvement was a refined equation of state. The use of this equation of 
state to calculate the collapse of a spherically symmetric protostar starting 
from a density of 10~*^ g cm~^ produces violent oscillations in central 
density and temperature after the stellar core has formed. The instability is 
triggered when the adiabatic exponent Ti = {din P/dln p)s falls below 4/3, 
and the source of the energy for the reexpansion is association of hydrogen 
atoms into molecules. 

In the two-dimensional case, the much higher starting density and 
the correspondingly higher mass inflow rate onto the core, as well as the 
effects of rotation, are sufficient to suppress the instability. A few relatively 
minor oscillations, primarily in the direction of the rotational pole, dampen 
quickly. The numerical procedure uses a grid that moves in the (spherical) 
radial direction and thus is able to resolve the central regions well, down 
to a scale of 10^° cm. This calculation is carried to the point where a 
fairly well-defined core of 0.07 M© has formed, which is still stable to 
non-axisymmetric perturbations (/? = 0.08). A surrounding disk structure 
is beginning to form, out to a radius of about 1 AU. The density and 
temperature in the equatorial plane at that distance are about 3 x 10"^ 
g cm~^ and 2500 K, respectively. Rirther accretion of material into the 
core region is likely to increase the value of /?. The calculation was not 
continued because of the large amount of computer time required. 

A different approach to the problem of the two-dimensional collapse 
of the protostar has been considered by Adams and Shu (1986) and Adams, 
et al. (1987). The aim is to obtain emergent spectra through frequency- 
dependent radiative transfer calculations. In order to bypass the difficulties 


of a full two-dimensional numerical calculation, they made several approxi- 
mations. The initial condition is a "singular" isothermal sphere, in unstable 
equilibrium, with sound speed c,, uniformly rotating with angular velocity 
n. In the initial state the density distribution is given by p <x R"^, where 
R is the distance to the origin, and the free-fall accretion rate onto a 
central object of mass M is given by M = 0.975 c,^/G. The hydrodynamical 
solution for the infalling envelope is taken to be that given by Tferebey et al. 
(1984), a semianalytic solution under the approximation of slow rotation. 
The thermal structure and radiation transport through the envelope can 
be decoupled from the hydrodynamics (Stabler et al. 1980). The model at 
a given time consists of an (unresolved) core, a circumstellar disk, and a 
surrounding infalling, dusty, and optically thick envelope. The radiation 
produced at the accretion shocks at the core and disk is reprocessed in 
the envelope, and emerges at the dust photosphere, primarily in the mid- 
infrared. The thermal emission of the dust in the envelope is obtained by 
approximating the rotating structure as an equivalent spherical structure; 
however, the absorption in the equation of transfer is calculated taking 
the full two-dimensional structure into account. The model is used to fit 
the observed infrared radiation from a number of suspected protostars, 
by variation of the parameters M, c„ Q, t]d, and r;,, where the last two 
quantities are the efficiencies with which the disk transfers matter onto 
the central star and with which it converts rotational energy into heat and 
radiation, respectively. These models provide good fits to the spectra of 
the observed sources for typical parameters M = 0.2 -1.0 Mq, c, = 0.2 - 
0.35 km s-\ n = 2 X 10"" - 5 x lO-'^ j^j s-\ rjo = 1 and tj. = 0.5. Of 
particular interest is the fact that in many cases the deduced values of n 
fall in the range j « 10^° cm^ s~\ which is appropriate for "solar nebula" 
disks. The contribution from the disk broadens the spectral energy distri- 
bution and brings it into better agreement with the observations than does 
the non-rotating model. More recent observational studies of protostellar 
sources (Myers et al. 1987; Cohen et al. 1989) also are consistent with the 
hypothesis that disks have formed within them. 


Full hydrodynamic calculations of the collapse, including frequency- 
dependent radiative transport, have recently been reported by Bodenheimer 
et al. (1988). The purpose of the calculations was to obtain the detailed 
structure of the solar nebula at a time just after its formation and to obtain 
spectra and isophotal contours of the system as a function of viewing 
angle and time. Because of the numerical difficulties discussed above, the 
protostar was resolved only on scales of 10^^ - 10*^ cm. These calculations 


have now been redone with the extension of the outer boundary of the 
grid to 5 X 10^^ cm, with improvements in the radiative transport, and 
with a somewhat better spatial resolution, about 1 AU in the disk region 
(Bodenheimer et al. 1990). 

The initial state, a cloud of 1 M© with a mean density of 4 x 10~'^ g 
cm~^, can be justified on the grounds that only above this value does the 
magnetic field decouple from the gas and allow a free-fall collapse, with 
conservation of angular momentum of each mass element, to start (Nakano 
1984; 'Rchamuter 1987). The initial density distribution is assumed to be a 
power law, the temperature is assumed to be isothermal at 20 K, and the 
angular velocity is taken to be uniform with a total angular momentum of 
10*^ g cm^ s~'. Because the cloud is ah-eady optically thick at the initial 
state, the temperature increases rapidly once the collapse starts. The inner 
region with R < 1 AU fe unresolved; the mass and angular momentum 
that flow into this core are calculated. At any given time, a crude model of 
this material is constructed under the assumption that it forms a Maclaurin 
spheroid. From a calculation of its equatorial radius R^, the accretion 
luminosity L = GMM/Rg is obtained. For each timestep At the accretion 
energy LAt is deposited in the inner zone as internal energy and is used 
as an inner boundary condition for the radiative transfer. Most of the 
energy radiated by the protostar is provided by this central source. During 
the hydrodynamic calculations, radiative transfer is calculated according 
to the diffusion approximation, which is a satisfactory approximation for 
an optically thick system. Rosseland mean opacities were taken from 
the work of Pollack et al. (1985). After the hydrodynamic calculations 
were completed, frequency-dependent radiative transfer was calculated for 
particular models according to the approach of Bertout and Yorke (1978), 
with their grain opacities which include graphite, ice, and silicates. 

The results of the calculations show the formation of a rather thick disk, 
with increasing thickness as a function of distance from the central object. 
As a function of time the outer edge of the disk spreads from 1 AU to 
60 AU, because of the accretion of material of higher angular momentum. 
The shock wave on the surface is evident, and the internal motions in the 
disk are relatively small compared with the collapse velocities. At the end 
of the calculation the mass of the disk is comparable to that of the central 
object, and it is not gravitationally unstable according to the axisymmetric 
local criterion of Tbomre (1964). The central core of the protostar, inside 
10^^ cm, contains about 0.6 M© and sufficient angular momentum so that 
f3 « 0.4. This region is almost certainly unstable to bar-like perturbations. 
Theoretical spectra show a peak in the infrared at about 40/i; when viewed 
from the equator the wavelength of peak intensity shifts redward from that 
at the pole. A notable difference between equator and pole is evident 
in the isophotal contours. At 40 fun, for example, the peak intensity 


shifts spatially to points above and below the equatorial plane because of 
heavy obscuration there. This effect becomes more pronounced at shorter 
wavelengths. Maximum temperatures in the midplane of the disk reached 
1500 K in the distance range 1-10 AU. At the end of the calculation, after 
an elapsed time of 2500 years, these temperatures ranged from 700 K at 2 
AU to 500 K at 10 AU and were decreasing with time. 


In the preceding example most of the infalling material joined the disk 
or central object on a short time scale, because of the high initial density. 
For a lower initial density, processes of angular momentum transport in 
the disk would begin before accretion was completed. The problem of 
the rapidly spinning central regions is apparently not solved by including 
angular momentum transport by turbulent viscosity during the collapse 
phase. Furthermore, no plausible physical mechanism for generating tur- 
bulence on the appropriate scale has been demonstrated. The angular 
momentum transport resulting from gravitational torques arising from the 
non-axisymmetric structure of the central regions is likely to leave them 
with values of /? near 0.2 (Durisen et al. 1986). Therefore, even further 
transport is required. A related mechanism has been explored by Boss 
(1985, 1989). He has made calculations of protostar collapse, starting from 
uniform density and uniform angular velocity, with a three-dimensional 
hydrodynamic code, including radiation transport in optically thick regions. 
Small, initial non-axisymmetric perturbations grow during the collapse, so 
that the central regions, on a scale of 10 AU, become significantly non- 
axisymmetric even before a quasi-equihbrium configuration is reached. The 
deduced time scales for angular momentum transport depend on the initial 
conditions but range from 10^ to Vf years for systems with a total mass 
of 1 M0. However, since the evolution has not actually been calculated 
over this time scale, it is not clear how long the non-axisymmetry will last 
or how it will affect the angular momentum of the central core. 

It is likely that some additional process is required to reduce j of the 
central object down to the value of 10^'^ characteristic of T Tburi stars. 
The approach of Safronov and Ruzmaikina (1985) is to assume that the 
initial cloud had an even smaller angular momentum (j « 10*® cm^ s"') 
than that assumed in most other calculations discussed here. The cloud 
would then collapse and form a disk with an equilibrium radius much less 
than that of Jupiter's orbit Outward transport of angular momentum into 
a relatively small amount of mass is then required to produce the solar 
nebula. Magnetic transport could be important in the inner regions, which 
are warm and at least partially ionized (Ruzmaikina 1981). However, out- 
side about 1 AU (Hayashi 1981) the magnetic field decays faster than it 


amplifies, and magnetic transport is ineffective. A supplementary mech- 
anism must be available to continue the process. One possibility is the 
turbulence generated in the surface layers of the disk, caused by the shear 
between disk matter and infalling matter. Another possibility is that the 
initial cloud had higher j, and the rapidly spinning central object is braked 
through a centrifugally driven magnetic wind which can remove the angular 
momentum relatively quickly (Shu et al. 1988). 

As far as the evolution of the disk itself is concerned, other important 
mechanisms that have been suggested include (a) gravitational instability; 
(b) turbulent viscosity induced by convection, and (c) sound waves and shock 
dissipation. The former can occur if the disk is relatively massive compared 
with the central star or if the disk is relatively cold. Although it is still an 
open question whether this instabiUty can result in the formation of a binary 
or preplanetary condensations, the most likely outcome is the spreading 
out of such condensations, because of the shear, into spiral density waves 
(Larson 1983). Lin and Pringle (1987) have estimated the transport time 
to be about 10 times the dynamical time. Processes (b) and (c) have time 
scales more in line with the probable lifetimes of nebular disks. Convective 
instability in the vertical direction (Lin and Papaloizou 1980), induced by 
the temperature dependence of the grain opacities, gives disk evolulionaiy 
times of about 10^ years (Ruden and Lin 1986). An alternate treatment of 
the convection (Cabot et al. 1987a,b) gives a time scale longer roughly by 
a factor of 10. Sound waves induced by various external perturbations give 
transport times in the range 10^ to 10^ years (Larson 1989). A complete 
theory of how the disk evolves after the immediate formation phase may 
involve several of the mechanisms just mentioned, and its development will 
require a considerable investment of thought and numerical calculation. 


This work was supported in part by a special NASA theory program 
which provides funding for a joint Center for Star Formation Studies at 
NASA-Ames Research Center, University of California, Berkeley, and 
University of California, Santa Cruz. Further support was obtained from 
National Science Foundation grant AST-8521636. 


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Three-Dimensional Evolution of 
Early Solar Nebula 

Alan P. Boss 
Carnegie Institution of Washington 


Mathematically speaking, solar nebula formation is an initial value 
problem. That is, it is believed that given the proper initial conditions and 
knowledge of the dominant physical processes at each phase, it should be 
possible to calculate the evolution of a dense molecular cloud core as it 
collapses to form a protosun and solar nebula. Also, through calculating 
the evolution of the dust grains in the nebula, it should be possible to 
learn how the initial phases of planetary accumulation occurred. While 
this extraordinarily ambitious goal has not yet been achieved, considerable 
progress has been made in the last two decades, with the assistance of 
current computational resources. This paper reviews the progress toward 
the goal of a complete theory of solar nebula formation, with an emphasis 
on three spatial dimension (3D) models of solar nebula formation and 

In principle, astronomical observations should provide the initial con- 
ditions required for theoretical calculations of solar nebula formation. This 
assumes that physical conditions in contemporary regions of solar-type star 
formation in our galaxy are similar to the conditions « 4.56 x 10^ years 
ago. Whether or not this is a reasonable assumption, considering that the 
age of the solar system is a fair fraction of the Hubble time, there really 
is no other means of constraining the initial conditions for solar system 

Millimeter wave and infrared telescopes have revealed that low-mass 
(solar-type) stars are presently forming preferentially in groups distributed 
throughout large molecular cloud complexes in the disk of our galaxy. These 



molecular clouds have complex, often filamentary structures on the largest 
scales (~l(X)pc). On the smallest scales (~0.1pc), where finite telescope 
resolution begins to limit the observations, molecular clouds are composed 
of centrally condensed cloud cores surrounded by cloud envelopes. The 
cloud cores are gravitationally bound and, should they begin to collapse 
upon themselves because of self-gravity, are quite likely to form stars 
(Myers and Benson 1983). Indeed, when infrared observations of embedded 
protostellar objects (presumed to be embedded pre-main-sequence T "Riuri 
stars or very young protostars) are combined with millimeter wave maps 
of molecular cloud cores, it appears that roughly one half of the cloud 
cores contain embedded protostars (Beichman et al. 1986). The physical 
conditions in molecular cloud cores, or their predecessors, should then 
provide the best indication of the initial conditions that are appropriate for 
solar nebula formation. 

Practically speaking, there are several reasons why astronomical obser- 
vations can only provide us with a range of possible initial conditions for 
solar nebula formation. First, since even the short time scales associated 
with low-mass star formation (~10^ - 10^ years) are quite long compared 
to human lifetimes, one can never be sure what a particular collapsing 
cloud core will produce. Second, although interferometric arrays have the 
potential to greatly increase our understanding of cloud core properties, 
the length scales appropriate for the initial phases of collapse are only 
marginally resolved by current millimeter wave telescopes. Third, because 
many (if not most) cloud cores have already collapsed to form protostars, 
their properties may not be appropriate for constraining the earliest phases 
of collapse. If the immediate predecessors of cloud cores could be identi- 
fied, then the constraints on the initial conditions for protostellar collapse 
would be improved considerably. 

Given these limitations, observations of cloud cores suggest the fol- 
lowing initial conditions for solar nebula formation: 1) Cloud cores have 
masses in the range of 0.1 to lOM©, implying that evolution within the 
molecular cloud complex has already reduced the mass of sub-structures by 
several orders of magnitude, from masses characteristic of giant molecular 
clouds (~10^ - IO^Mq), to masses in the stellar range; 2) Dense cloud 
cores have maximum densities on the order of 10~^^ - 10"'® g cm~^, 
sizes less than 0.1 pc, and temperatures close to lOK. These are basically 
the same initial conditions that have long been used to model protosolar 
collapse (Larson 1969). 

One of the remaining great uncertainties is the amount of rotation 
present in cloud cores, because even the most rapidly rotating clouds have 
Doppler shifts comparable to other sources of line broadening, such as 
thermal broadening, translational cloud motions, and turbulence. While 
there is strong evidence that at least some dense clouds rotate close to 


centrifugal equilibrium (specific angular momentum J/M ~ 10^' cm^s~^ 
for solar mass clouds), it is unknown how common such rapid rotation is, 
or how slowly clouds can rotate. Three-dimensional calculations (described 
in the next sub-section) indicate that the initial amount of rotation is 
critical for determining whether clouds collajKC to form single or multiple 

Finally, most three-dimensional calculations of protostellar collapse 
have ignored the possible importance of magnetic fields, in no small part 
because of the computational dilficulties associated with their inclusion in 
an already formidable problem. OH Zeeman measurements of magnetic 
field strengths in molecular clouds yield values (~30/jG) in cool clouds 
implying that magnetic fields dominate the dynamics on the largest scales 
(~10 - lOOpc). However, there is evidence from the lack of correlations 
between magnetic field directions and dense cloud minor and rotational 
axes that, on the smaller scales (and higher densities) of dense cloud cores, 
magnetic fields no longer dominate the dynamics (Heyer 1988). Loss of 
magnetic field support is probably caused by ambipolar diffusion of the ions 
and magnetic field lines during contraction of the neutral bulk of the cloud. 
The evidence for decreased importance of magnetic fields at densities 
greater than ~10~^'' g cm"^ suggests that nonmagnetic models may be 
adequate for representing the gross dynamics of solar nebula formation. 


The first numerical models of the collapse of interstellar clouds to 
form solar-type stars disregarded the effects of rotation, thereby reducing 
the problem to spherical symmetry and the mathematics to one-dimensional 
(ID) equations (Bodenheimer 1968). The assumption of spherical symme- 
tiy ensures that a single star will result, but unfortunately such calculations 
can say nothing about binary star or planet formation. The first major dy- 
namical problem in solar nebula formation is avoiding fragmentation into 
a binary protostar. 

Larson (1969) found that ID clouds collapse non-homologously, form- 
ing a protostellar core onto which the remainder of the cloud envelope 
accretes. Once the envelope is accreted, the protostar becomes visible as 
a low-mass, pre-main-sequence star (T Tkuri star). Models based on these 
assumptions have done remarkably well at predicting the luminosities of T 
Tiiuri stars (Stabler 1983). However, there is a recent suggestion (T^char- 
nuter 1987a) that the protostellar core may not become well established 
until much later in the overall collapse than was previously thought The 
ID models also showed that the first six or so orders of magnitude increase 


in density during protostellar collapse occur isothermally, a thermodynam- 
ical simplification employed in many of the two-dimensional (2D) and 
three-dimensional (3D) calculations that followed. 

The first models to include the fact that interstellar clouds must have 
finite rotation were restricted to two dimensions, with an assumed sym- 
metry about the rotation axis (axisymmetry) being assumed (Larson 1972; 
Black and Bodenheimer 1976). These models showed that a very rapidly 
rotating, isothermal cloud collapses and undergoes a centrifugal rebound in 
its central regions, leading to the formation of a self-gravitating ring. While 
a similar calculation yielded a runaway disk that initially cast doubt on the 
physical reality of ring formation (Norman et al. 1980), it now appears that 
most of the ring versus disk controversy can be attributed to differences in 
the initial conditions studied and to the possibly singular nature of the stan- 
dard test problem. With a single numerical code. Boss and Haber (1982) 
found three possible outcomes for the collapse of rotating, isothermal, 
axisymmetric clouds: quasi-equilibrium Bonnor-Ebert spheroids, rings, and 
runaway disks, with the outcome being a simple function of the initial con- 
ditions. TVvo-dimensional clouds with initially high thermal and rotational 
energies do not undergo significant collapse, but relax into rotationally flat- 
tened, isothermal equilibrium configurations that are the 2D analogues of 
the ID Bonnor-Ebert sphere. High specific angular momentum 2D clouds 
that undergo significant collapse form rings, while slowly rotating 2D clouds 
(J/M < 10^° cm^ s""*) can collapse to form isothermal disks (Tferebey et al. 

Whereas the Sun is a single star, a cloud that forms a ring is likely 
to fragment into a multiple protostellar system (Larson 1972). Because of 
this, subsequent axisymmetric presolar nebula models have concentrated 
on slowly rotating clouds (Ticharnuter 1978, 1987b; Boss 1984a). These 
models, which included the effects of radiative transfer and detailed equa- 
tions of state, showed that even for a very slowly rotating cloud, formation 
of a central protosun is impossible without some means of transporting 
angular momentum outward and mass inward. Consequently, 'Bchamuter 
(1978, 1987b) has relied on turbulent viscosity to produce the needed an- 
gular momentum transport, even during the collapse phase, when there are 
reasons to doubt the efficacy of turbulence (Safronov 1969). 

Because isothermal protostellar clouds, and even slowly rotating non- 
isothermal clouds (Boss 1986), may fragment prior to ring formation (Bo- 
denheimer et al. 1980), a 3D (i.e., fully asymmetric) calculation is necessary 
in order to ensure that a given collapsing cloud produces a presolar nebula 
rather than a binary system. Fbrming the presolar nebula through forma- 
tion of a triple system followed by orbital decay of that triple system to yield 
a runaway single nebula and a close binary does not appear to be feasible 
(Boss 1983), because the runaway single nebula is likely to undergo binary 


fragmentation during its own collapse. Hence 3D models of solar nebula 
formation have also concentrated on low J/M clouds, in a search for clouds 
that do not undergo rotational fragmentation during their isothermal or 
nonisothermal coUapse phases. Three-dimensional calculations, including 
radiative transfer in the Eddington approximation, have shown that solar 
mass clouds with J/M < 10^° cm^ s'^ are indeed required in order to avoid 
binary formation (Boss 1985; Boss 1986). 

There are two other ways of suppressing binary fragmentation other 
than starting with insufficient J/M to form and maintain a binary protostel- 
lar system. First, when the initial mass of a collapsing cloud is lowered 
sufficiently, fragmentation is halted, yielding a lower limit on the mass of 
protostars formed by the fragmentation of molecular clouds of around 0.01 
M© (Boss 1986). The minimum mass arises from the increased importance 
of thermal pressure as the cloud mass is decreased; thermal pressure re- 
sists fragmentation. This limit implies that there may be a gap between 
the smallest mass protostars ("brown dwarfs") and the most massive plan- 
ets (the mass of Jupiter is « 0.001 M©)- Second, clouds that are initially 
strongly centrally condensed can resist binary fragmentation simply because 
of their initial geometric prejudice toward forming a single object (Boss 
1987). While initially uniform density and initially moderately condensed 
clouds readily fragment, given large J/M and/or low thermal pressure, it 
appears to be impossible to fragment a cloud starting from an initial power 
law density profile (see Figure 1). Considering that the majority of stars are 
found in binary or multiple systems, it does not appear likely that power 
law initial density profiles are widespread in regions of star formation, but 
such a profile could have led to solar nebula formation. Thus, the 3D 
calculations have shown that formation of the Sun requires the collapse of 
either a very slowly rotating, high-thermal energy cloud, or else the collapse 
of a cloud starting from a power law initial density profile. In contrast to 
ID calculations, however, no 3D calculation has been able to collapse a 
cloud core all the way to the pre-main-sequence. In part, this is because 
of the greatly increased computational effort necessary to evolve a mul- 
tidimensional cloud through the intermediate phases. Equally important 
though, is the problem that when rotation is included, accumulation of 
the central protosun requires an efficient mechanism for outward angular 
momentum transport. Identifying this mechanism and its effects is one of 
the major remaining uncertainties in solar nebula models. 


Given the formation of a rotationally flattened, presolar nebula through 
the collapse of a cloud core that has avoided binary fragmentation, the next 
major dynamical problem is accumulating the protosun out of the disk 



FIGURE 1 Density contours in the midplane of three models of protostellar collapse with 
varied initial density profiles (Boss 1987). The rotation axis falls in the center of each plot; 
counterclockwise rotation is assumed. Each contour represents a factor of two change in 
density; contours are labelled with densities in g cm~^. (a) Initially uniform density profile, 
(b) initially Gaussian density profile, and (c) initially power law profile (r~^). As the initial 
degree of central concentration increases, the amount of nonaxisymmetry produced during 
collapse decreases. Quantitatively similar results hold when the initial cloud mass or initial 
angular velocity is decreased; binary formation is stifled. Diameter of region shown: (a) 
580 AU, (b) 300 AU, (c) 110 AU. 



matter. Angular momentum must flow outward, if mass is to accrete onto 
the protosun, and also if the angular momentum structure of the solar 
system is to result from a cloud with more or less uniform J/M. The 
physical process responsible for this dynamical differentiation is thought to 
have operated within the solar nebula itself, rather than in the material 
collapsing to form the nebula. 

Three different processes have been proposed for transporting mass 
and angular momentum in the solar nebula: viscous shear, magnetic 
stresses, and gravitational torques (see also Bodenheimer, this volume). 
Molecular viscosity is far too small to be important, so turbulent viscosity 
must be invoked if viscous stresses are to dominate. The most promising 
means for driving turbulence in the solar nebula appears to be through 
convective instability in the vertical direction, perpendicular to the neb- 
ula midplane (Lin and Papaloizou 1980). The main uncertainty associated 
with convectively driven viscous evolution, aside from the effective strength 
of the turbulent stresses, is the possibility that such a nebula is unstable 
to a diffusive instability that would break up the nebula into a series of 
concentric rings (Cabot et al. 1987). 

As previously mentioned, magnetic fields need not be dominant during 
the early phases of presolar collapse, and frozen-in magnetic fluxes scale 
in such a way that they never become important, if they are not important 
initiaUy. While some meteorites show evidence for remanent magnetic 
fields requiring solar nebula field strengths on the order of 30/iT (Sugiura 
and Slrangway 1988), the magnetic pressure (B^/Stt) corresponding to such 
field strengths is still considerably less than even thermal pressures in hot 
solar nebula models (Boss 1988), implying the negligibility of magnetic 
fields for the gross dynamics of the solar nebula. 

The remaining candidate for angular momentum transport is gravi- 
tational torques between nonaxisymmetric structures in the solar nebula. 
Possible sources of nonaxisymmetry include intrinsic spiral density waves 
(Larson 1984), large-scale bars (Boss 1985), and triaxial central protostars 
(Yuan and Cassen 1985). Early estimates of the efficiency of gravitational 
torques (Boss 1984b) implied that a moderately nonaxisymmetric nebula 
can have a time scale for angular momentum transport just as short as 
a strongly turbulent accretion disk. Three-dimensional calculations of the 
aborted fission instability in rapidly rotating polytropes (Durisen et al. 1986) 
were perhaps the first to demonstrate the remarkable ability of gravitational 
torques to remove orbital angular momentum from quasi-equilibrium, non- 
axisymmetric structures similar to the solar nebula. 

At later phases of nebula evolution, nonaxisymmetry and spiral density 
waves can also be driven by massive protoplanets. The possible effects range 
from gap clearing about the protoplanet, in which case the protoplanet must 
evolve along with the nebula (Lin and Papaloizou 1986), to rapid orbital 


decay of the protoplanet onto the protosun (W^rd 1986). While the effects 
of viscous or magnetic stresses can be studied with 2D (axisymmetric) solar 
nebula models, in order to model the effects of gravitational torques, a 
nonaxisymmetric (generally 3D) solar nebula model must be constructed. 


Only a few attempts have been made at studying the nonaxisymmetric 
suucture of the early solar nebula. Cassen et al. (1981) used a type of 
N-body code to study the growth of nonaxisymmetry in an infinitely thin, 
isothermal model of the solar nebula. Cassen et al. (1981) found that 
when the nebula is relatively cool (~100K) and more massive than the 
central protosun, nonaxisymmetry grows within a few rotational periods, 
resulting either in spiral arm formation, or even fragmentation into giant 
gaseous protoplanets in the particularly extreme case of a nebula 10 times 
more massive than the protosun. Cassen and Tbmley (1988) are presently 
engaged in using this code to study the onset of gravitational instability in 
nebula models with simulated thermal gradients. 

Boss (1985) used a 3D hydrodynamics code to model the early phases 
of solar nebula formation through collapse of a dense cloud core, and 
found that formation of a strong bar-like structure resulted. However, 
because the explicit nature of the code limited Boss (1985) from evolving 
the model very far in time, these results are only suggestive of the amount of 
nonaxisymmetry that could arise in the solar nebula. Recently, Boss (1989) 
has tried to circumvent this computational problem by calculating a suite of 
3D models starting from densities high enough to bypass the intermediate, 
quasi-equilibrium evolution phases that obstruct explicit codes. While these 
initial densities for collapse (~10~^^ - 10~'^ g cm~^) are clearly not 
realistic given the present understanding of star formation, it can be argued 
(Boss 1989) that starting from these high densities should not greatly distort 
the results. 

The 3D models of Boss (1989) show that gravitational torques can be 
quite efficient at transporting angular momentum in the early solar neb- 
ula. The models show that collapsing presolar clouds become appreciably 
nonaxisymmetric (as a result of a combination of nonlinear coupling with 
the infall motions, rotational instability, and/or self-gravitation), and that 
trailing spiral arm patterns often form spontaneously; trailing spiral arms 
lead to the desired outward transport of angular momentum. The most 
nonaxisymmetric models tend to be massive nebulae surrounding low mass 
protosuns in agreement with the results of Cassen et al. (1981). Extrap- 
olated time scales for angular momentum transport, and hence nebula 
evolution, can be as short as ~10^ years for strongly nonaxisymmetric mod- 
els, or about ~10® - lO'^ years for less nonaxisymmetric models. Because 


these time scales are comparable to or less than model ages for naked 
T Tkuri stars (Walter 1988), solar-type, pre-main-sequence stars that show 
no evidence for circumstellar matter, it appears that gravitational torques 
can indeed be strong enough to account for the transport of the bulk of 
nebula gas onto the protosun on the desired time scales. While these initial 
estimates are encouraging, it remains to be learned exactly how a solar 
nebula evolves due to gravitational torques. 


The 3D solar nebula models of Boss (1989) show little tendency for 
breaking up directly into small numbers of giant gaseous protoplanets, 
contrary to one of the models of Cassen et cd. (1981). This difference 
is probably a result of several features of the Boss (1989) models. The 
inclusion of 3D radiative transfer means that the compressional heating 
accompanying nebula formation can be included, leading to considerably 
higher temperatures than assumed in Cassen et al. (1981), and hence 
greater stability against break-up. Also, the gradual buildup of the nebula 
through collapse in the Boss (1989) models means that incipient regions of 
gravitational instability can be sheared away into trailing spiral arms by the 
differential rotation of the nebula before the regions become well-defined. 
These models thus suggest that planet formation must occur through the 
accumulation of dust grains (Safronov 1969; Wetherill 1980). 

Considering that dust grain evolution is not yet included in 3D codes, 
detailed remarks about the earliest phases of dust grain accumulation are 
not possible. However, the models of Boss (1989) can be used to pre- 
dict surface densities of dust grains in the solar nebula, and these surface 
densities are quite important for theories of planetary accumulation. For 
example, Goldreich and Ward (1973) suggested that a dust surface density 
at 1 AU of <Td ~ 7.5 g cm~^ would be sufficient to result in a gravitational 
instability of a dust sub-disk (Safronov 1%9) that could speed up the inter- 
mediate stages of planetary accumulation. More recently, Lissauer (1987) 
has proposed the rapid formation of Jupiter through runaway accretion of 
icy-rock planetesimals in a nebula with o-<j > 15 g cm~' at 5 AU. Rapid 
formation is required in order to complete giant planet formation prior to 
dispersal of the solar nebula. Using a gas to dust ratio of 200:1 at 1 AU and 
50:1 at 5 AU, these critical surface densities correspond to gas surface den- 
sities of 1500 g cm-^ at 1 AU and 750 g cm-^ at 5 AU. Similar minimum 
densities are inferred from reconstituting the planets to solar composition 
(Weidenschilling 1977). The models of Boss (1989) have surface densities 
in the inner solar nebula that are nearly always sufficient to account for 
terrestrial planet formation. However, surface densities in the outer solar 
nebula are less than the critical amount, unless the nebula is quite massive 



FIGURE 2 Density cnntouis in the midplane of three solar nebula models formed by 
collapse onto protosuns with varied initial masses M, (Boss 1989), plotted as in Figure 
1. (a) M, = 1 M0, (b) M, = 0.01 Mq, (c) M, = OMq. The initial nebula mass was 

1M0 for eadi model, and the initial specific angular momentum was J/M - 6.2 X 
cm s 



The resulting nebulae become increasingly nonaxisymmetric as the initial protosun 
mass is decreased; (b) forms trailing spiral arms that result in efficient transport of angular 
momentum, while (c) actually fragments into a transient Unary system. These models also 
illustrate the ability of a massive central object to stabilize a protostellar disk. Region 
shown is 20 AU across for each model. 


(~lMo). Any protoJupiter that is formed rapidly in a massive nebula is 
likely to be lost during subsequent evolution, either because gap clearing 
will force the protoplanet to be transported onto the protosun with the rest 
of the gas (Lin and Papaloizou 1986), or because motion of the protoplanet 
relative to the gas will result in orbital decay onto the protosun (Ward 
1986). The planetary system is the debris leftover from formation of the 
voracious Sun, and so prematurely formed protoplanets are at peril. 

Variations in the initial density and angular velocity profiles do not 
appear to be able to produce sufficiently high surface densities at 5 AU in 
low-mass solar nebula (Boss 1989), so it does not appear that the surface 
densities required for planet formation can be accounted for simply by 
collapse onto a nebula. Diffusive redistribution of water vapor could pref- 
erentially accumulate ices wherever temperatures drop to 160K (Stevenson 
and Lunine 1988), but this mechanism can only be invoked to explain the 
formation of one of the outer planets. The most promising means for 
enhancing surface densities of the outer solar nebula appears to be through 
nebula evolution subsequent to formation. Viscous accretion disks can 
increase the surface density in the outer regions where the angular momen- 
tum is being deposited (Lin and Bodenheimer 1982; Lissauer 1987). While 
the long-term evolution of a 3D nebula subject to gravitational torques 
is as yet unknown, gravitational torques should produce a similar result 
(Lin and Pringle 1987). Determining the evolution of a nonaxisymmetric 
solar nebula thus appears to be a central issue in finding a solution to the 
problem of rapid Jupiter formation. 

Finally, the 3D models of Boss (1988, 1989) have important implica- 
tions for the thermal structure of the solar nebula. Provided the artifice of 
starting from high initial densities does not severely overestimate nebula 
temperatures, it appears that the compressional energy released by infall 
into the gravitational well of a solar-mass object can heat the midplane of 
the inner solar nebula to temperatures on the order of 1500 K for times on 
the order of 10* years. Such temperatures are high enough to vaporize all 
but the most refractoiy components of dust grains. In particular, because 
the vaporization of iron grains around 1420 K removes the dominant source 
of opacity, temperatures may be regulated to values close to ~1500 K by 
the thermostatic effect of the opacity. A hot inner solar nebula can account 
for the gross depletion of volatiles on the terrestrial planets (relative to 
solar) by allowing the volatiles to be removed along with the H and He of 
the nebula. Hot solar nebula models were introduced by Cameron (1962) 
in one of the first solar nebula investigations, but have since fallen into 
disfavor (Wood 1988), so it will be interesting to see whether high tempera- 
tures in the iimer nebula can be successfully resurrected, and whether they 
will prove to be useful in explaining planetary and asteroidal formation. 



This research was partially stipported by U.S. National Aeronautics 
and Space Administration grant NAGW-1410 and by U. S. National Science 
Fbundation grant AST-85 15644. 


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■Pf9l-22964 ' 

Formation and Evolution of the Protoplanetary Disk 


Schmidt Institute of the Physics of the Earth 


The structure of the solar system, the similarity of isotope compositions 
of its bodies (in terms of nonvolatile elements), and observational data on 
the presence of disks (and possibly of planets) around young solar-type stars 
are evidence of the joint formation of the Sun and the protoplanetary disk. 
The removal of angular momentum to the periphery (necessary for the 
formation of the Sun and protoplanetary disk) is possible at the formation 
stage in the center of the contracting cloud (protosolar nebula) of the 
stellar-like core (Sun's embryo). The possibility that the core forms before 
fragmentation begins to impose a constraint on the value of the angular 
cloud momentum. This value is highly dependent on the distribution of 
angular momentum within the cloud. 

This paper discusses a disk formation model during collapse of the 
protosolar nebula with J ~ lO^^g cm^s"', yielding a low-mass protoplan- 
etary disk. The disk begins to form at the growth stage of the stellar-like 
core and expands during accretion to the present dimensions of the solar 
system. Accretion at the edge of the disk significantly affects the nature of 
matter fluxes in the disk and its thermal evolution. 

In addition to the internal heat source (viscous dissipation), there is 
an external one which affects the temperature distribution in the disk: 
radiation (diffused in the accretion envelope) of the shock wave front at 
the core and in the nearest portion of the disk. Absorbed in the disk's 
surface layers, this radiation heats these layers, and reduces the vertical 
temperature gradient in the disk to a subadiabatic point. It also renders 
convection impossible. Convection becomes possible after accretion ceases. 




The proximity of planes of planetary orbit in the solar system indi- 
cates that planets were formed in the thin, elongated protoplanetary disk 
surrounding the young Sun. 

The coincidence of isotope compositions of the Sun, the Earth, and 
meteorites for basic nonvolatile elements, and the similarity of the chemical 
compositions of the Sun and Jupiter are evidence that the Sun and the 
protoplanetary disk originated from the same concentration of interstellar 
medium. In view of observed data on the rapid (~ 10® ^ lO'^ years) removal 
of gas from the proximity of solar-type stars which had formed (T Tkuri 
stars), it is natural to infer that the convergence of the isotope composition 
of the Sun and the planets also means that they formed contemporaneously. 

According to the theory developed by Jeans early in this century, stars 
are formed as a result of collapse under the impact of the gravitational 
effects of compacted regions of the interstellar medium. The collapse 
occurs when the forces of self-gravity exceed the sum of forces restricting 
compression. The latter include the thermal pressure gradient, magnetic 
pull, and centrifugal forces. Data from infrared and radioastronomy tell 
us that the stars are formed in molecular clouds: low temperature regions 
(~ 10 K) with relatively high density 10-^^ H- 10"^° g • cm"^, in which 
hydrogen and other gases (besides the noble gases) are in a molecular state, 
and condensing matter is included in grains. 

Study of the radio lines of molecules has shown that the clouds are 
highly inhomogeneous. They contain compact areas, cores with densities 
p ~ 10~^° -r 10"*^ g ■ cm~^ and masses M ~ 0.1 -=- 10 M©, infrared 
sources and compact zones of ionized hydrogen with ages iC -=- 10^ years. 
Relatively weak, variable T Tkuri stars are also seen in certain molecular 
clouds. They approximate the Sun in terms of mass (0.5 -^ 2Mq), but 
are much younger, with ages 10^ -r 10® years (Adams et al. 1983). Their 
formation is related to the compression of cores of molecular clouds under 
the impact of the forces of self -gravity. 

Contemporary theory of evolution holds that the fate of a star is 
determined by its mass and chemical composition. In view of the similarity 
of these parameters, we can identify T l&xxii stars with the young Sun and 
use observed data on these stars to construct a theory of the formation of 
the Sun and the protoplanetary disk. 


Elongated, disk-shaped, gas-dust envelopes with characteristic masses 
O.IM© (Sargent and Beckwith 1987; Smith and Tbrrile 1984) have been 
discovered around several young stars (HL TSu, DG Tiiu, p Pic, and a 


source of infrared radiation L 1551 IRS5). The radii of the gas-dust disks, 
which were determined by eclipses of the stars, are estimated at ~ 10 -^ 
10^ AU (see Strom's article in this volume). The radii of the disk-shaped 
envelopes in CO molecule lines are estimated on the order of ICP AU. 
Data from observations of the IRAS infrared astronomical satellite have 
shown that 18% of 150 near stars which have been studied exhibit infrared 
excesses. That is, they emit more in the infrared range than matches their 
temperatures (Backman 1987). It was proven for a number of closer stars 
(Aumann et al. 1984) that excess infrared radiation is not created by the 
star itself, but by the envelope of dust grains. The grains absorb the light 
of the star and reemit it in the infrared range. It is possible that disks exist 
for all stars which exhibit infrared excesses (Bertrout et al. 1988). Thus, 
there is a greater probability that the formation of a star is accompanied 
by the formation of a gas-dust disk around it. 

IRAS discovered in the envelopes of stars a Lyr, a PsA, and /? Pic that 
the central region with a radius of 30 AU is dust-free (Backman 1987). This 
empty region could not have been retained after the star's formation stage, 
since the dust grains from the surrounding envelope shift inside under the 
Poynting-Robertson effect and fill up the empty space over a time scale of 
< 10^ years. This is too brief a time scale in comparison with the age of 
the star. A possible cause of the existence of an empty region around stars 
is that the large planetesimals and planets may remove those dust grains 
shifting towards the center. 

The first finding of the search for planets around solar-type stars was 
obtained using an indirect search method: determining with high accuracy 
(up to 10 to 13 metere per second) the ray velocities of the nearby stars. 
Seven of 16 stars examined were found to have long-period Doppler Shifts 
of velocities with amplitudes of 25-45 meters per second. It is probable 
that these variations in ray velocities are produced by invisible components 
(planets with masses from one to nine Jovian masses) moving in orbit 
around the stars (Campbell et al. \98&). 

These findings, together with observational data on the disks around 
young stars, are evidence that the formation of the planetary system is a 
natural process which is related to star formation. 


The most likely cause of the formation of protoplanetary disks and 
planetary systems, including the solar system, is the rotation of molecular 
clouds. The rotation of clouds and separate dense regions in them is a 
function of the differential rotation of the galaxy and turbulence in the 
interstellar medium. The rotation velocities of molecular clouds and their 
nuclei are determined by the value of the gradient of the spectral line's ray 


velocity along the cloud profile. Angular velocities of rotation n, measured 
in this manner, are included in the interval 10~^^-10~^^s"' (Myers and 
Benson 1983). For small cores of < O.lpc, rotation is only measurable for 
n > Z10~'''s~*. Rotation was not discovered with this kind of accuracy 
for approximately 30% of the cores. 

Angular momentum value and internal distribution J(r) are important 
cloud/core characteristics for star formation. These characteristics depend 
both on the value Q on the outer edges of the cloud and its internal distri- 
bution. Data on the dependence n(r) have been measured for individual, 
sufficiently elongated molecular clouds. Thus, for cloud B 361, fi ~ const 
in the inner region and falls on the periphery in the outer region (Arquilla 
1984). A concentration of matter towards the center is also observed within 
the compact cores. The distribution fi is not known. The maximum laws 
of rotation which appear to be reasonable are being explored in theoretical 

n = const with p = const, (la) 

a = const with p oc r~^. (16) 

The first describes the angular momentum distribution in a homoge- 
neous and solid-state rotating cloud. It holds for a core which has separated 
from the homogeneous rotating medium where the specific angular mo- 
mentum of each cloud element is conserved. The second corresponds to a 
solid-state rotating, singular isothermal sphere. This is an isothermal cloud 
with p = Cj/(2irGr^), in which the forces of self-gravity are balanced out 
by internal pressure (C, is the speed of sound). In order for this kind 
of distribution to be established, the core must exist long enough during 
the stage preceding collapse for angular momentum redistribution to occur 
and for solid-state rotation to be established. The characteristic time scale 
for the existence of cores prior to the onset of contraction is r,y~~10'^ 
years. This is significantly more than the contraction of an individual core 
of Tff ~~ 10® years (Adams et al. 1983). 

Random (turbulent) motion with near-sound speeds is present in the 
cores (Myers 1983). The viscosity created by this motion may be represented 
as (Schakura and Sunyaev 1973) 

i^ = l/Suj/j ~ a i?c,, (2) 

where R denotes the core radius, sc is the speed of sound in it, oc is the 
nondimensiona lvalue, and v^ and Ij are the characteristic turbulent motion 
velocity and scale. The time scale for angular momentum redistribution in 
the core under the effect of viscosity r^ ~ R^/i/r. The condition r^ ~ t,j 
is fulfilled for 


oc ~i?/c,r,y. (3) 

As a numerical example, let us consider the core TMC-2 . It has a 
mass M ~ M©, c, = 310^cm/s and vx ~ 0.5 c„ R ~ 0.1 pc (Myers 1983). 
Substitution in (2) and (3) of these numerical values and t,j = 3 10"s give 
us oc ~ 0.03. This fits with Ij-ZR ~ 0.1. This estimate demonstrates that the 
efiiciency of angular momentum redistribution in various cores may differ 
depending on the scale of turbulent motion. Therefore, cores with both 
rotation laws, (see la and lb) and the intermediate ones between them, 
may exist. 

The angular momentum of a solid-state rotating spherical core of mass 
M is equal to 

J ^ lO^^K—^ (^Y' f in i/ .y '\cm^s-\ (4) 
10~^'s-i \MqJ \10 '^(jfcm ■*/ 

where k = 2/5 and 2/9 for the rotation laws (la) and (lb), and p denotes 
the mean core density. 

The rotation of clouds plays an important role in star formation. Stellar 
statistics demonstrate that more than one half >, 60%) of solar-type stars 
enter into binary or multiple systems which, as a rule, exhibit angular 
momentums > 10^^ gcm^s"' (Kraycheva et al. 1978). This means that 
when a binary (multiple) system is formed, the bulk of a cloud's angular 
momentum is concentrated in the orbital movement of stars relative to 
each other. The formation of a single star with a disk is an alternative and 
additional route by which a forming star expels excess angular momentum. 

In a circumsolar Kepler disk, the angular momentum per unit mass is, 
actually, j = (GMoR)'/2. At a Jovian distance (5 AU) j ~ lO^^cm^ s'K 
This is 100 times more than the maximum possible and 10* times more than 
the present angular momentum related to the Sun's rotation. Therefore, 
even a low-mass but elongated disk can accumulate a large portion of cloud 
angular momentum, thereby allowing a single star to form. 

Estimates of mass Md and angular momentum J© of a circumstellar 
protoplanetary disk, performed by adding presolar composition dissipated 
hydrogen and helium to the planet matter, yielded (Weidenschilling 1977), 

IQ-^Mo <Md^ 10-*MQ,and 3 • lO" < J^ < 2 • 10^^^ • cm'^ ■ s'^ 
that is, 



Using a system of two bodies with constant aggregate mass and full 
angular momentum as an example, Lynden-Bell and Pringle (1974) demon- 
strated that the system's total energy decreases as mass is transferred from 
the smaller to the larger body, and the concentrations of angular mo- 
mentum in orbital motion are less than the massive body. Consequently, 
dissipation of rotational energy, accompanied by removal of the angular 
momentum to the periphery and its concentration in a low amount of mass, 
is necessary to form a single star with a protoplanetary disk as a cloud 

Effectiveness of angular momentum redistribution is the key issue of 
protoplanetary disk formation. The high abundance of binary or multiple 
stars of comparable masses and the analysis of the contraction dynamics 
of rotating clouds indicate that angular momentum redistribution is not 
always effective enough for a single star with a disk to be formed. The 
entire process, from the beginning contraction all the way to the formation 
of a star, has thus far only been examined for a nonrotating cloud (Larson 
1969; Stabler et al. 1980). Calculations have shown that the initial stage of 
contraction occurs at free-fall velocities and is accompanied by an increase 
in the concentration of matter towards the center. Pressure increase, 
coupled with a rise in temperature, triggers a temporary deceleration in the 
contraction of a cloud's central region within a density range of pc ~ 10"'^ 
-^ 10~* g-cm~^. This is followed by one more stage of dynamic contraction 
that is initiated by molecular hydrogen dissociation. Dissociation terminates 
at 10" ^g cm"^; the contraction process again comes to a halt; and a 
quasihydrostatic stellar-like core is formed with an initial mass of M^ ~ 
1O~^M0 and central density pc ~ 10~^gcm~^. This core is surrounded by 
an envelope which initially contains 99% mass and falls onto the core over 
a time scale of 10^-^ 10^ years. Naturally, a single nonrotating diskless star 
is formed from the contraction of this kind of protostellar cloud. 

It is clear from these general ideas that contraction of a rotating 
protostellar cloud occurs in a similar manner, when the centrifugal force 
in a cloud is low throughout in comparison to the gravitational force and 
internal pressure gradient. 

The role of rotation is enhanced with increased density in the con- 
traction process where angular momentum is conserved. (For example, 
the ratio of rotational energy to gravitational energy is j9 oc p^l^ for a 
spherically symmetrical collapse). 'Rvo-dimensional and three-dimensional 
calculations for the contraction of rapidly rotating protostellar clouds have 
shown that as a certain Per is reached in the cloud central region, a ring 
(two-dimensional) or nonaxisymmetrical (three-dimensional) instability de- 
velops. According to Bodenhemier (1981) and Boss (1987) this instability 
triggers fragmentation: Per — 0.08 for ring instability at the hydrodynamic 


contraction stage (Boss 1984). Naturally, the smaller the angular momen- 
tum of the cloud's central region, the later the instability arises. It has 
been suggested that a cloud's fate depends significantly on the stage of 
contraction at which instability arises: the cloud turns into a binary or mul- 
tiple star system when /3cr is attained at the initial hydrodynamic stage of 
contraction (with pc ;S 10" '^ gcm-^). it becomes a single star with a disk 
when nontransparency increases, causing the contraction of the portion to 
decelerate before instability develops. The condition that a nontranspar- 
ent core be formed before fragmentation occurs, imposes a constraint on 
the cloud angular momentum: J < 10^^ g cm^s"^ for rotation law (la) 
(Safronov and Ruzmaikina 1978; Bcks 1985). 

Ragmentation may be halted by a sufficiently efficient removal of angu- 
lar momentum from the center. Tbrbulence or the magnetic field (Safronov 
and Ruzmaikina 1978) have been proposed as removal mechanisms. An- 
other is gravitational friction (Boss 1984) generated from excitation by a 
central nonaxisymmetrical condensation of the density wave in the envelope 
surrounding the core. Yet to be determined is whether angular momentum 
removal at this stage can actually prevent fragmentation. The difficulty is 
that contraction deceleration due to enhanced nontransparency is tempo- 
rary. It is followed by the stage of hydrodynamic contraction triggered by 
molecular hydrogen dissociation. During this stage, density increases by 
several orders and /? may attain I3„- The formation of a single star with 
a disk (or without it) appears to be highly probable when the cloud (or 
its central portion, to be more exact) exhibit such a slight angular momen- 
tum that instability does not develop until the formation of a low-mass, 
stellar-like core with Mc < IQ-^Mq (Ruzmaikina 1980, 1981). When it 
is born, the core must be magnetized as a result of enhancement of the 
interstellar magnetic field during contraction (Ruzmaikina 1980, 1985). The 
poloidal magnetic field strength in the stellar-like core is estimated at 10 
-^ 10^ Gauss. This field ensures angular momentum redistribution in the 
core over a time scale less than its evolution time scale ( > 10^ years) and 
initiates an outflow of the core's matter, forming an embryonic disk instead 
of fragmentation. 

With disruption of the core's axial symmetry, angular momentum 
removal to the periphery may also be carried out by the spiral density 
wave generated in the envelope (Yuan and Cassen 1985). Consequently, 
the formation of a single, stellar-like core appears to be sufficient for the 
formation of a single star. 

The possibility of the formation of a stellar-like core with M^ ~ 
10" 'M© imposes constraints on the maximum value of the protostellar 
cloud's angular momentum. With an angular momentum distribution within 
the cloud as described in ratio (la) (solid-state rotation with homogeneous 


density), the maximum angular momentum value of the cloud at which a 
single, stellar-like core can form is within the range (Ruzmaikina 1981) 

0.3 10"(M/Mo)'/^ < J^„ < 2 lQ^\MlMQfl\ (5) 

With the law of rotation contained in (lb) (solid-state rotation with 
p (X r~2), Jmaar IS approximately (Mq/M^)^/^ ~ 500 times greater than with 
(la), that is, J^„ > > lO^'^g cm^s"' with M = IM©. This is easy to 
determine by equating the angular momentums of the central sphere with 
mass Mc ~ 10~^Mo, for distributions (la) and (lb), respectively. 

It follows from the above estimates that: (1) single stellar-like cores 
can be formed during the contraction of clouds whose angular momenta 
are included in a broad range. This range overlaps to a large degree the 
angular momentums of cores in molecular clouds. Therefore, there may 
be a considerably high probability that a single, stellar-like core can be 
formed in the contracting dense region (core) of a molecular cloud. This 
depends on the angular momentum distribution established inside the core 
of molecular clouds at the pre-contraction stage; (2) J^^j, approximates or 
exceeds by several times the angular momentum of a "minimal mass" solar 
nebula (Weidenschilling 1977). J*,,,,, is greater than or on the order of the 
angular momentum of a massive solar nebula (Cameron 1%2). Let us note 
that the idea of a massive solar nebula was recently revived by Marochnik 
and Mukhin (1988), who reviewed the estimate of the Oort cloud's mass 
on the hypothesis that the typical mass of cometary bodies in the cloud is 
equal to the mass of Halley's comet. (Data gathered by the Vega missions 
have put estimates of its mass at two orders greater than was previously 

For a broad range of J values, scenarios appear possible whereby a 
single Sun embiyo is first formed in the contracting protosolar nebula. A 
disk then forms around it. Disk parameters and the nature of its evolution 
are dependent on angular momentum value. However, the presence of a 
single, stellar-like core in the center has a stabilizing effect on the disk's 
central portion and may prevent its fragmentation. We will later discuss in 
more detail a protoplanetary disk formation model with cloud contraction of 
J ~ lO^^g cm^ s"^ which appears preferable for a solar nebula (Ruzmaikina 
1980, 1982; Ruzmaikina and Maeva 1986; see also review papers Safronov 
and Ruzmaikina 1985; Ruzmaikina et al. 1989). 


Let us consider the stage of protosolar nebula contraction when a 
single, stellar-like core and a compact embryonic disk are formed in the 
center, both surrounded by an accretive shell. The embryonic disk could 


have been formed from external equatorial core layers under the impact of 
magnetic pull (Ruzmaikina 1980, 1985) or by direct accretion of the rotating 
envelope at a distance from the axis greater than the equatorial radius of the 
core (Tfereby et al. 1984). The directions of flow of the accretive material 
intersect the equatorial plane inside the so-called centrifugal radius R/t 
which exceeds (at least at the final stage of accretion) the radius of the 
protosun R<. = 3 -^ 5 R© 


Rk = 0.15 -^ 0.5 AU where M = 1 M©, J == lO^^gcm^-s-S and K = 2/5 
^ 2/9, respectively. 

A mechanism for the coformation of the Sun and the protoplanetaiy 
disk during protosolar nebula contraction with J ~ lO^^g cm^s"' has been 
proposed in studies by Ruzmaikina (1980) and Cassen and Moosman (1981) 
and investigated by Ruzmaikina (1982), Cassen and Summers (1983), and 
Ruzmaikina and Maeva (1986). The disk proposed in these models is a 
turbulent one. The following points have been offered to justify this: large 
Reynolds number ( ^ 10'°) for currents between the disk and the accretive 
envelope and currents generated by differential disk rotation; and the 
possible development of vertical (Z) direction convection. Investigations 
have shown that a sufficiently weak turbulence with oc ~ 10"^ can trigger 
an increase in the disk radius to the current size of the solar system within 
the time scale of the Sun's formation (10* years). Approximately 1% of 
the kinetic energy of the accretive material is needed to support this kind 
of turbulence. Near-sound turbulence produces disk growth to 10^ AU. 

It is noteworthy that the process of disk growth occurs inside the 
protosolar nebula as it continues to contract. Nebula matter (gas and dust) 
accrete on the forming Sun and the disk (Figure 1). Matter situated in the 
envelope and close to the equatorial plane encounters the face of the disk. 
Tbrbulence causes accreting matter flowing about the disk to mix with disk 
matter. Addition of the new matter is especially effective on the face, where 
this matter falls on the disk almost perpendicular to the surface. It loses its 
radial velocity in the shock wave and is retarded long enough for effective 
mixing. Complete mising on the remaining surface of the disk only occurs 
in layer Ah. This layer is small at subsonic turbulence in comparison with 
disk thickness Ah/h ~ a'/^ (Ruzmaikina and Safronov 1985). Ruzmaikina 
and Maeva (1986) looked at the process of protoplanetary disk formation 
for a model with J = 2 ■ 10"g cm^- s~^ and M = I.IM©, taking into 
account accretion of material both to the Sun and to the disk. Turbulence 
viscosity in the disk was alleged to equal vx = (1 -=- 6)' 10'* (M/M©- R 
AU)'/2 cm^s-'. This fits with oc w 3 • 10"^ -=- 4 • 10" ^. As a result, by the 
completion of the accretion stage (which lasts 10^ years), the disk radius 




Schematic profile of a forming ptotoplanetary disk immersed in an accretion 

was equal to 24 - 70 AU, its mass is about 0.1 Mq, and the remaining mass 
is concentrated in the Sun. The distribution of radial \Jr velocity of matter 
flow in the disk undergoes a complex evolution: at the initial stage, matter 
in the larger portion of the disk flows towards the center. The velocity is 
only positive near the disk edge. However, there gradually emerges one 
more area with a positive radial velocity which is broadening over time. 
1\vo regions with \Jr < 0; R < R, ~ 0.3 ^ 0.5 AU and 0.6 Rp < R < 0.95 
R/) two regions with \5r > 0; R, < R < 0.6 R^ and R > 0.95 Rd exist in 
the disk by the time accretion is completed. 


The question of temperature distribution and fluctuation in the disk is 
important for an understanding of the physical and chemical evolution of 
preplanetaiy matter. Tfemperattire greatly affects the kinetics of chemical 
reactions, matter condensation, and vaporization, the efficiency rate at 
which dust grains combine during collision, and the conditions within 


The protoplanetary disk is thin, that is, at any distance R from the 
center, the inequality h/R < 1 is true for the thickness of a disk's ho- 
mogeneous atmosphere of h = c,Q~^. Therefore, heat transfer occurs 
primarily transversely to the disk in the 1-c-z direction, between the central 
plane and the surface. At the same time, a disk of mass 10~^- IO'^Mq 
and radius 10 - 100 AU is optically thick (Lin and Papaloizou 1980). 
Therefore, if there is an internal source heating the disk, the temperature 
in the central plane is higher than on the surface. Such a source is the 
internal friction in conditions of differential rotation. Mechanical energy 
dissipation in the disk is proportional to ^>rR^(dn/dR)^. If we propose 
turbulence as a viscosity mechanism, the viscosity value averaged for disk 
thickness could be written using Schakura and Sunyaev's oc-parameter as 
i/T =(x c,h where the speed of sound is taken from the central plane. As 
we noted above, the value a must equal 10~^ for a disk to form over 
10^ years. A number of models were constructed using Lynden-Bell and 
Pringle's viscous disk evolution theory (1974). These models considered 
the further evolution of the protoplanetary disk after protosolar nebula 
matter has stopped precipitating on it. A large portion of disk mass is 
transported inside and accretes to the Sun at this stage. At the same time 
the disk radius increases owing to conservation of the angular momentum. 
According to the estimates, surface density decreases by one order over 
10^ years with oc= 10~^. (Ruden and Lin 1986; Makalkin and Dorofeeva 

Internal disk structure and, in particular, the vertical temperature pro- 
file were also considered for this stage (viscous disk diffusion). Lin and 
Papaloizou's model (1980) proposes 2^direction convection as a turbulence 
mechanism in the disk. Correspondingly, the temperature gradient in this 
direction is slightly higher than adiabatic. P-T conditions and matter con- 
densation in the protoplanetary disk's internal portion (Cameron and Fegley 
1982) were calculated on the basis of this model. Cabot et al. (1987) yielded 
a more accurate vertical structure which accounts for the dependence of 
opacity on temperature: beginning with the central plane, the conveclive 
layer with a superadiabatic temperature gradient is superseded at a higher 
elevation by a layer in which the gradient is below adiabatic. One more 
layer alternation may occur above this if the photosphere temperature is 
below that of ice condensation. However, on the average, the tempera- 
ture profile is quite close to adiabatic for the entire thickness of the disk. 
Tfemperature distributions in these models are in fairly close agreement 
with the temperature estimate generated by Lewis (1974) where he used 
cosmochemical data. His estimate is indicated by the crosses in Figure 2. 

Convective models only take into account the internal source of proto- 
planetary disk heating: turbulence dissipation. However, external sources 
may provide an appreciable input to disk heating. They are particularly 





R, A.U. 

FIGURE 2 Temperature dislribution in the central plane of the protoplanetary disk: 1 is 
the maximum temperatures at the disk formation stage. The figures 2, 3, and 4 are at the 
subsequent stage of viscous disk evolution (from the study by Makalkina and Dorofeeva 
1989): 2 is 110^ yearx after the stage begins; 3 is 210^ years later, and 4 is after 10 
years. Ranges of temperature ambiguities as per Lewis' cosmochemical model (1974) are 
indicated by the overlapping areas. 

significant during disk formation. At the accretion stage of contraction of 
a protosolar nebula with J ~ lO^gcm^s-S energy is emitted at the shock 
front of the protosolar core's surface and the portion of the disk with R^ 
~ 10^- centimeters nearest to it (which is only several times greater than 
the core radius and two to three orders less than the radius of disk Rd by 
the end of the accretion stage). This radiation is absorbed and reemilted in 
the infrared range in the accretion envelope around the core. A significant 
portion of the disk is immersed in the envelope's optically thick portion 
and is appreciably heated by its radiation (Makalkin 1987). With a charac- 
teristic accretion time scale t^ ~ 10^ years, the radius of the optically thick 


portion of the accretion envelope (the radius of the dust photosphere) is 
approximately 10" centimeters. 

This estimate was made for a spherically symmetric collapse model 
(Stabler et al. 1981). However, it is just in terms of the order of value 
and for a model with a moderate angular momentum. The estimate of the 
internal radius of the optically thick portion of the envelope (the radius 
of the dust vaporization front), which is approximately 10'^ centimeters 
(Figure 1), is also true. Where there is a disk around the core, a very rough 
estimate of luminosity L = GMcM/Rt, and a more stringent estimate based 
on the theory of Adams and Shu (1986), demonstrate that energy ensuring 
a luminosity value L ~ 20 -^ 25L0 is emitted at the shock front near the 
core (R < R^) with r^ w 10^ years and J w lO^^gcm^ s-^ That is, this 
value is several times less than in Stahler et al.'s spherically symmetrical 
model (1980) where L = 66Lo. An estimate of the temperature in the 
envelope using Adams and Shu's method (1985) produces for L ~ 20 ^ 
25Lo a temperature in the envelope of T„„ ~ 1100 K at R = 1 AU. 
We note for comparison that at the same R Ten„ ~ 1600 K with L = 70 
Lq and Te„„ = 800 K at L = 15L© (for the spherical model of Adams 
and Shu (1985) with Va ^ 10® years). The exact form of the shock front 
surface and the dependence of the radiation flow on angular coordinates 
are still unknown. It is considered in a zero approximation that at R > 
Ri, isotherms have a near spherical form. 

The specific dissipation energy of turbulent motion in the protoplane- 
tary disk can be expressed as D = 9/4 purQ^. It follows from this that the 
flow of radiant energy from the disk (per unit of area of each of the two 
surfaces in its quasistationary mode) is equal to Di = 9^i; vt Q^ = <t T^^jj 
where E denotes the disk's surface density, and a is the Stefan-Boltsman 
constant. It is easy to see that at oc ~ 10~^ the effective disk temperature 
Tejj is significantly lower than the temperature in the accretion envelope 
Te„« at the same R. Therefore, the effect of outflow from the disk to heat 
the envelope at R > R* can be disregarded. Even where a developed 
convection is present, the flow of radiant energy inside the protoplanetaiy 
disk F is approximately three times greater than the convective value (Lin 
and Papaloizou 1985). This is similar to what occurs in hot accretion disks. 
TTie solution to the formula for radiation transport in the disk dF/dz = 
D, where the mean opacity is dependent on temperature according to the 
power law, A'e oc T ^ is expressed as (Makalkin 1987) 

(T,/r.)^-« = 1 + 3/64 (4 - OiDi/aT^)^^.!:, (7) 

where T, and T, denote temperatures in the disk's central plane and on 
its surface, Ke, = Ke(T,). In the absence of external heating sources, 
T, = Te// is fulfilled and, correspondingly, Di = aT^. In the case of 



a disk immersed in the accretion envelope, T, in formula (7) is equal to 
the temperature in the envelope Ten„ at the same R. Te„„ is several times 
greater than T,//, and hence, Di < aT*,. The mean opacity Ke, examined 
by Pollack et al. (1985) for a protoplanetary disk, taking into account the 
chemical composition and dimensions of dust grains, can be approximated 
as a function T* with various values of ^ in different temperature intervals. 
Below the temperature of dust condensation, the values of ^ range from 
0.6 - 1.5. Above this temperature Lin and Papaloizou's approximation 
(1985) can be used for 1(1(1). The ratio (7) can be applied not only to 
the entire thickness of the disk, but also to its different layers in order to 
account for variations in the function Ke(J). Then S and Di correspond 
to the appropriate layer, and T^ and T, to its lower and upper boundaries. 
We note that formula (7) differs significantly both in its appearance and its 
result from the widely accepted, simplified formula (To/T,)"* = 3^ Ke„T,, 

where TUo - T<^iT„). 

Curve 1 in Figure 2 illustrates the temperature in the disk's central 
plane at the end of its formation stage. We calculate this temperature 
using formula (7) for the disk model, (Ruzmaikina and Maeva 1986) with 
values = 110*gcm-2 and vt = 1.210*5cm2s-i at R = 1 AU. This accounts 
for the fact that E mt «: R~^^^ is everywhere except the disk center and 
edge. The temperature in the accretion envelope is estimated for L = 25 
Lq. The plateau in curve 1 fits that part of the disk where its vertical 
structure is two-layered. A dust-free (owing to its high temperature) layer 
is located around the central plane. The mean opacity here is two orders 
lower (and the vertical temperature gradient is commensurately low), than 
in the higher, colder layer. This colder layer contains condensed dust 
grains. The vertical profile of this portion of the disk is represented in 
Figure 1. It is clear from Figure 1 that the condensation front has a curved 
shape. Computations have shown that for all R i lO^"* centimeters the 
inequality To < 2T, is fulfilled. It follows, in particular from this, that the 
vertical temperature gradient at the disk formation stage is noticeably lower 
than the adiabatic value calculated in many studies. There is, therefore no 

V^tyazev and Pechernikova (1985) and Ruzmaikina and Safronov 
(1985) estimated the maximum for additional heating of matter as it falls 
onto the disk surface; in the shock wave (where it had been) and via 
aerodynamic friction of the dust The effect is relatively insignificant in the 
area R » Ri, R ;S 10^'' centimeters. Thus, the dust temperature does 
not exceed 600 K for 1 AU with J ~ 10'^ g • cm^ • s-^ That is, it is much 
lower than the temperature inside the disk (Curve 1, Figure 2). 

Solar radiation falling at a low inclination on its surface (Safronov 
1969) is an external source of disk heating after accretion of the envelope 
to the protosun and disk is completed. It should be taken into account 


together with turbulence (an internal source) when calculating temperature 
in the disk. T, in (7) is determined at this stage by the formula (tT^ = Di+ 
F,, where F, denotes the solar energy flux absorbed by the disk surface. 
It follows from the computations of Makalkin and Dorofeyeva (1989) that 
Di > F, everywhere for R ^ 0.1 AU. The vertical temperature gradient 
is only higher than the adiabatic where dust grains are not vaporized. 
Where there is no dust, low opacity T(e < 10~^cm^g~' generates a veiy 
low-temperature gradient. The temperature distribution is then close to 
isothermic. With this in mind, the authors calculated a combined (adiabat 
- isotherm) thermodynamic model of a protoplanetary disk. Figure 2 
(Curves 2, 3, and 4) illustrate the temperature distributions in the central 
plane generated in this model for different points in time. Tfemperatures 
as per Lewis' cosmochemical model (1S>74) are a good fit with calculated 
temperatures for the time interval (2-5) • 10^ years. 

TTiis model of protoplanetary disk formation predicts a significantly 
different solid matter thermal history: vaporization and subsequent con- 
densation of dust grains in the internal region of the solar system as it forms, 
and the conservation of interstellar dust (including organic compounds and 
ices) in the peripheral (greater) portion of the planetary system. These 
predictions are in qualitative agreement with cosmochemical data and, in 
particular, with the latest data on Halley's comet (Mukhin et al. 1989). 
According to estimates of thermal conditions in the disk, the radius of the 
zone of vaporization of silicate and iron dust grains (T ^ 1400 K) reached 
1-2 AU. However, matter which passes through a vaporization region as 
the disk forms is dispersed to a larger region. This is a consequence of 
both the mean, outwardly-directed flux of matter in the internal portion of 
the disk (Ruzmaikina and Maeva 1986), and turbulent mbcing. 


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Physical-Chemical Processes in a 
Protoplanetary Cloud 

AVGUSTA K. Lavrukiiina 
VI. Vernadskiy Institute of Geochemistry and Analytic Chemistry 


According to current views, the protosun and protoplanetary disk were 
formed during the collapse of a fragment of the cold, dense molecular 
interstellar cloud and subsequent accretion of its matter to a disk. One of 
the most critical cosmochemical issues in this regard is the identification 
of relics of such matter in the least altered bodies of the solar system: 
chondrites, comets, and interplanetary dust. The presence of deuterium- 
enriched, carbon-containing components in certain chondrites (Pillinger 
1984) and radicals and ions in comets (Shulman 1987) is evidence that 
this area holds great promise. If a relationship is established between 
solar nebula and interstellar matter, we can then identify certain details, 
such as the interstellar cloud from which the Sun and the planets were 
formed. We can also come to a deeper understanding of the nature of 
physico-chemical processes in the protoplanetary cloud which yielded the 
tremendous diversity of the chemical and mineralogical compositions of the 
planets and their satellites, meteorites, and comets. 


One would expect that chemical compositions of interstellar clouds 
are significantly varied and are a function of such physical parameters 
as temperature and density. Moreover, one would expect that they are 
also dependent on the age of a cloud, its history, the impoverishment of 



elements, the flux of the energy particles of cosmic rays and photons, and 
the flow of material emanating from stars located in or adjacent to a cloud. 

Several objects have been studied in the greatest detail at this time 
(Irvine et al. 1987): (1) The core of the KL region of the Orion nebula. 
It contains at least four identifled subsources with varying chemistry. (2) 
The central galactic cloud Sgr B2. It is the most massive of all the known 
gigantic molecular clouds and contains high-luminosity stars. (3) The cold, 
dark, low-mass clouds, TMC-1 and L134N. They have substructures with 
individual "lumps" with a mass of several M©. It has been suggested that 
such areas correspond to locations where solar-type stars were formed. 
TMC-1, in particular, matches that portion of ring material which is pre- 
dicted by the rotating molecular cloud collapse model. (4) Clouds in the 
spiral arm. These are sources of HII areas or are the remnants of su- 
pernova CaSA. (5) The expanding envelope of the evolving carbon star, 
IRC -I- 10216 (CWLeO). Tkble 1 provides data on 80 molecules which 
were discovered by 1988 in the interstellar medium. Of these, 13 are new 
and three are the cyclical molecules, C3H2, SiC2 and C-C3H. A maximum 
high deuterium-enrichment D/H w 10^ x (D/H)^o,m (Bell et al. 1988) is 
characteristic for the first of these. The ratio [CsHDj/fCaHa] lies within 
the range 0.05-0.15 for 12 dark, cold (approximately lOK) clouds. The 
first phosphorus compound (PN) discovered in the interstellar medium is 
among the new molecules. Phosphorus nitride has been discovered in three 
gigantic molecular clouds and, in particular, in the Orion nebula. In the 
Orion nebula it associates with dark gas flowing from the infrared source 
IRc2. This is most likely a protostar. PN abundance is low, while the search 
for other phosphorus compounds (PH3, HCP, and PO) has yet to meet with 
success. This may seem strange, because P abundance in diffuse clouds 
approaches cosmic levels. However, many metals and S are impoverished 
because they are among the constituents of dust grains. 

Data relating to the discovery of NaCl, AlCl, KCl, and AlF in envelopes 
of evolving stars are of tremendous interest. The carbon star IRC -H0216 
is an example. The distributions of these compounds are in agreement 
with calculations of chemical equilibria for the atmospheres of carbon- 
rich stars (C/O > 1) in the area T = 1200-1500K. In addition to the 
molecules indicated above, SiH4, CH4, H2C=CH2, CH=CH, SiC2 have 
been discovered in the envelopes of stars. The latter molecule is particularly 
interesting: it broadens the range of molecules which condense at C/O > 
1. Data on the search for O2 in six dark clouds are also evidence of the 
presence of dark clouds which characterize an oxygen insufficiency. 

TWo important consequences follow from the data contained in Tkble 1. 
(1) The obviously nonequilibrious nature of interstellar chemistry. Evidence 
of this is the presence of highly reactive ions and radicals with one or 
two unpaired electrons. (2) The presence of numerous molecules with 



TABLE 1 Identification of Interstellar Molecules (Irvine 1988) 

Simple hydrides, oxides, sulfides and other molecules 




















HNO 7 

Nitrides, derivative 

acetylenes, and other molecules 





CN H2C=CH2' 











HjC-(C>0,-CN7 HN=C=0 





Aldehydes, alcohols 

, ethers, ketones. 

amides, and other molecules 
















Cyclical molecules 





























(a) New molecules discovered after 1986 are underlined, 
(x) Present only in clouds of evolving surs. 
(7) Not yet confiimed. 


unsaturated bonds, despite the fact that hydrogen distribution rates are 
three to four orders greater than for C, N, and O. This is evidence of the 
predominance of kinetic over thermodynamic factors in chemical reactions 
in the interstellar medium and of the large contribution of energy from 
cosmic rays and UV radiation to these processes. Chemically saturated 
compounds such as CH3CH2CN are only present in the "warmer" sources 
(i.e., in Orion). HNCO, CH3CN, HC3N, C2H3CN, C2H5CN levels are 
higher in warm clouds, possibly owing to higher NH3 parent molecule 

One interesting feature pertaining to the distribution rates for certain 
interstellar molecules is their uniformity for dark molecular clouds with wide 
variation in P and T parameters. Furthermore, an inverse dependence 
of the amount of gas molecules on dust density is absent This would 
have been an expected consequence of molecules freezing into the ice 
mantle of particles. This is confirmed by data on the constancy of the 
CO/dust ratio in three clouds. It is further supported by the absence of 
a drop in H2CO levels as dust density rises in dark molecular clouds. 
An indication that the efficiency rate of this in-freezing is not uniform 
for various molecules has also not been confirmed. A high degree of 
homogeneity of the H^^CO/^^CO and C2H/13C0 ratios for many clouds 
has been found. Clearly, the processes involved in the breakdown of particle 
ice mantles are highly efficient. Their efiiciency may be enhanced when 
dust grain density increases as the grains collide with each other. 

Data on the distribution of different interstellar molecules are in 
general agreement with calculations in which ion-molecular reactions in 
gas are the primary process. However, there is a question as to the 
reliability of calculations with a value of CO < 1 in a gas phase. It has 
been found that the abundance values for many C-rich molecules and ions 
are extremely low in steady-state conditions. Despite the fact that various 
explanations of these facts have been offered, an alternative hypothesis 
suggests that C/O > 1 in the gas phase. Other facts were already indicated 
above which can be explained by such a composition of the gas phase. 
Enhanced carbon levels may be attributed to the fact that CH4 (being a 
nonpolar molecular) is more easily volatilized from the surface of the grain 
mantle than NH3 and H2O. 

Therefore, we can hypothesize that in certain dark molecular clouds or 
in different portions of them, the gas phase has a C/O ratio which departs 
from the cosmic value. This is fundamentally critical to understanding the 
processes in the early solar system. It has been found that many unique 
minerals of enstatite chondrites (including enstatite, silicon-containing ka- 
masite, nainingerite, oldgamite, osbornite, and carbon) could only have 
been formed during condensation from gas with C/O > 1 (Petaev et al. 


1986). SiC and other minerals, which were condensed in highly reduc- 
ing conditions, have also been found in CM-type carbonaceous chondrites 
(Lavnikhina 1983). 


According to current thinking (Voshchinnikov 1986), the total sum of 
molecules in a "dense," not-too-hot gaseous medium of complex molecular 
composition precipitates into a solid phase, thereby forming embryos of 
dust grains. These grains then begin to grow through accretion of other 
molecular compounds or atoms. The grains may in turn act as catalysts for 
reactions to form new types of molecules on their surface. A portion of 
these remains as particles, and the rest converts to the gaseous phase. 

Laminated interstellar grains are formed in this manner. Their cores 
are made up of refractory silicate compounds, metal iron, and carbon. The 
grain mantle is formed from a mixture of ices of water, ammonia, methane, 
and other low-temperature compounds with varying admixtures. Atomic 
carbon may also be adsorbed on the mantle surface at the low temperatures 
of dark molecular clouds. These dust grains are often aspherical. Their size 
is approximately 0.3 ^m. Generation of the finest particles ( < 0.01 fita) 
also takes place. They have no mantle due to the increased temperature 
of these grains as a single photon is absorbed or a single molecule is 
formed. The dust grains are usually coalesced as a result of photoelectron 
emission and collisions with electrons and ions. Mean grain temperature is 
approximately 10 K 

The following data are evidence of the chemical composition of dust 


(1) IR- absorption band: 

A 3.1 /im - ice HjO (NH3), 

A A 9.7 and 18 fun - amorphous silicates, 

A A 4.61 and 4.67 urn - molecules with the groups ON and CO, 

A A 3.3 -r 35 /im - molecules with the groups CH2- and -CH3. 

(2) Emission spectra: 

A 11.3 fiia - SiC, 

A 30 /im - mixtures of MgS, CaS, FeSj, 

A 3.5 /im - formaldehyde (H2CO), 
six emission bands with A A 3.28 -r 11.2 /im -r- large organic molecules (Nc 

(3) A 22OOA -=- graphite (?), carbines (-C=C-), amorphous and glassy 



According to current views, at least part of the interstellar molecules 
is formed from reactions on dust grain surfaces. At low-grain surface 
temperatures and moderately high gas temperatures, atoms and molecules 
coming into contact with the surface may adhere to it. Van-der-Vaals 
effects determine a minimum binding energy value. However, significantly 
high values are also possible with chemical binding. Migration along the 
grain surface of affixed atoms generates favorable conditions for molecule 
formation. A portion of the released binding energy (Ec) of atoms in a 
molecule is taken up by the crystal grid of the grain surface. If the remaining 
portion of the molecule's energy is greater than Ec, the molecule "comes 
unglued" and is thrown into the gas phase. This process is accelerated 
when the dust grains are heated by cosmic rays. H2, CH4, NH3, and H2O 
molecules are formed in this manner. Since the binding energy of C, N, 
O, and other atoms is on the order of 800 K, they adhere to the grain 
surface where they enter into chemical reactions with hydrogen atoms. The 
aforementioned molecules are thus formed. Part of these then "comes 
unglued," such as the H2 molecule. A portion freezes to the grain surface. 
The temperatures at which molecules freeze are equal to (K): H2 - 2.5, 
N2 - 13, CO - 14. CH4 - 19, NH3 - 60, and H2O - 92. Hence, the 
formation of the mantle of interstellar dust grains and certain molecules in 
the gaseous phase of dense, gas-dust clouds occurs contemporaneously. 

Tkble 2 lists certain data on the characteristics of the basic physical 
and chemical processes involved in the formation and subsequent evolution 
of interstellar dust grains and the astrophysical objects in which these 
processes occur. With these data we can evaluate the nature of processes 
occurring in the protoplanetary cloud during the collapse and subsequent 
evolution of the Sun. These basic processes triggered: 1) the breakdown 
and vaporization of dust grains under the impact of shock waves at collapse 
and the accretion of primordial cloud matter onto the protoplanetary disk; 
2) the collision of particles; and 3) particle irradiation by solar wind ions. 
The role of these processes varied at different distances from the protosun. 
Yet the main outcome of the processes is that organic, gas-phase molecules 
and the cores of dust grains (surrounded by a film of high-temperature 
polymer organic matter) are present throughout the entire volume of the 
disk. They are obvious primary-starting material for the formation of a 
great variety of organics which are observed in carbonaceous chondrites 
(Lavrukhina 1983). Dust grains at great distances from the protosun (R 
^ 2 AU) will be screened from the impact of high temperatures and solar 
radiation. They will therefore remain fairly cold in order to conserve water 
and other volatile molecules in the mantle composition. Comets, obviously, 
contain such primary interstellar dust grains. 



TABLE 2 Characlcrislics of the Basic Physico-Chemical Processes of Interstellar Dust Grain 



Proposed Chemical 
Compounds or Processes 


Condensation of T=1400- Amorphous silicates, mixes 

high temperature -1280K of oxides MgO, SiO, CaO, 

embryos FeO, Fe, Ni-particles, 

SiC, carbines, graphile(7) 
amorphous & glassy caibon 

1) Atmospheres of cold surs 

2) Planeury nebulae 

3) Envelopes of novae 
and supemovae, 

4) Envelopes rf red giants 

2. Formation of 


FeS, H,0, 

1) Upper layers of cold stars 

mantle on 

NH, H,0, CH, X H,0 

and inl?rstellar space. 


S<did clatrates Ar, 

2) Dispersed matter of 

Kr, Xe. Carbines 

old planeury nebulae, 

3) GMC," 

4) Old supemovae envelopes 

3. Coalescence of 

t - lOyrs 

Ice with phenocrysts 

Turbulent gas 

fine particles 

from silicates, metals 

of protosiellar 

with formation of 

graphite (7) 


"sleeve" pooding 

type particles 

4. Destruction of 

Particle life- 

1) Collision of particles 

1) Envelopes <rf red giants 

dust grains 

span: ice- 

with V > 20kmc-'. 

and novae. 

(primarily in 


2) Sublimation, 

2) Shock waves from super- 


years, silicate- 

3) Physical and Chemical 

novae flash. 



3) Irradiation by high 


4) Photodesotption 

velocity ions of stellar 
wind and by high energy 
cosrruc rays in GMC^' 
and planeury nebulae 

5. Oxidation-reduc- 


FeO, Fe,0„ 


tion reactions 



interstellar medium 

on grain surface 

Fe oxidation 
by monatomic 

Formation of 

T=2.5-5 K 

FeH, FeH,, hydrides 

Dark GMC« zones 


of transitional metals 

6. Formation (rf 

Radiation poly- 

Tcdines, hexamelhylenl- 

UV -radiation. 

envelopes and 

merization of 

etramine, cellulose. 

costmc rays. 

dust from solid 


complex organic or 

shock waves in GMC?*' 


compounds with prebiological compounds 


1>4K on grains (PAC) 
with subsequent 

breakdown intc 



(x) Gigantic dark molecular interstellar clouds 



Investigation of the isotope composition of H, O, C, N, and the inert 
gases in meteorites, planets, and comets is extremely relevant as we attempt 
to understand the processes involved in the genesis of the preplanetaty 
cloud. The majority of these elements had a high abundance in the 
interstellar gas and the gas-dust, initial protosolar cloud. Great variation 
in the isotope composition for various cosmic objects is also characteristic 
of these elements. Such variation has made it possible to refute outmoded 
views of the formation of the protosolar cloud from averaged interstellar 
material (Lavrukhina 1982; Shukolyukov 1988). 

From detailed studies of meteorites, we have been able to discover 
a number of isotopically anomalous components and identify their carrier 
phases (Anders 1987). These studies have demonstrated that the pro- 
tomatter of the solar system was isotopically heterogeneous. For example, 
examination of the hydrogen isotope has shown that objects of the solar 
system can be subdivided into three groups in terms of the hydrogen isotopy 
(Eberhardt et al. 1987). (1) Deuterium-poor interstellar hydrogen, proto- 
solar gas, and the atmospheres of Jupiter and Saturn; (2) deuterium-rich 
interstellar molecules (HNC, HCN, and HCO+) of dark molecular clouds 
of Orion A; and (3) the atmospheres of Earth, Titanus, and Uranus, the 
water of Halley's comet, interplanetary dust, and certain chondrite frac- 
tions of Orgueil CI and Semarkona LL3 occupy an intermediary position. 
Clearly, the isotopic composition of hydrogen in these components is de- 
termined by the mixing of hydrogen from two sources: a deuterium-poor 
and a deuterium-rich source. A single gas reservoir is thus formed. 

A similar situation has been found for oxygen. IVvo oxygen compo- 
nents have been discovered in meteorites: impoverished and enriched ^®0 
of nucleogenetic origin (Lavrukhina 1980). The relative abundance of oxy- 
gen isotopes in chondrules tells us that chondrite chondrules of all chemical 
groups are convergent in relation to a single oxygen reservoir, characterized 
by the values S i«0 = 3.6 ± 0.2L% and 6 ^^0 = 1.7 ± 0.2L% (Lavrukhina 
1987; Clayton et al. 1983). They are similar to the corresponding values for 
Earth, the Moon, achondrites, pallasites, and mesosiderites. On the basis 
of these data and the dual-component, isotopic composition of nitrogen, 
carbon, and the inert gasses (Levskiy 1980; Anders 1987), workers have 
raised the idea that protosolar matter was formed from several sources. For 
example, two reservoirs of various nucleosynthesis are proposed that differ 
in terms of their isotopic composition and the degree of mass fractioniza- 
tion (Lavrukhina 1982; Levskiy 1980). Shukolyukov (1988) proposes three 
sources: ordinary interstellar gas; material injected into the solar system by 


an explosion of an adjacent supernova; and interstellar dust made up of a 
mixture of different stages of stellar nucleosynthesis. 

The presence of at least two sources of matter in protoplanetary 
matter may be evidence of the need to reconsider the hypothesis of the 
contemporaneous formation of the Sun and the protoplanetary cloud from 
a single fragment of a gigantic molecular interstellar cloud. 


Anders, E.A. 1987. Local and exotic oomponenU of primitive meteorites and their origin. 

TVans. R. See Lend. A323(l):287-304. 
Bell, M.B., L.W Avery, H.E. Matthews et al. 1988. A study of C3HD in cold interstellar 

clouds. Astrophys. J. 326(2):924-930. 
Clayton, R.N., N. Onuma, Y. Ikeda. 1983. Oxygen isotopic compositions of chondrules in 

Allende and ordinaty chondrites. Pages 37-43. In: King, E.A. (ed.). Chondrules and 

Their Origins. Lunar Planet. Institute, Houston. 
Eberhardt, P, R.R. Hodges, D. Krankowsky et al. 1967. The D/H and 180/160 isotopic 

ratios in comet Halley. Lunar and Planet. Sci. XVIII:251-252. 
Irvine, W.M. 1988. Observational astronomy: recent results. Page 14. Preprint, Five College 

Ratio Astronomy Observatory. University of Massachusetts, Amherst. 
Irvine, WM., P.F. Goldsmith, and A. Hjalmatson. 1987. Oiemical abundances in molecular 

clouds. Pages 561-609. In: Hollenbach, DJ, and H.A. Thronson (eds.). Interstellar 

Processes. D. Reidel Publishing Company, Dordrecht. 
Lavnikhina, A.K. 1987. On the origin of chondniles. Pages 75-77. In: XX Nat. Meteorite 

Conference: Thes. Paper. GEOKHI AS USSR, Moscow. 
Lavrukhina, A.K. 1983. On the genesis of carbonaceous chondrite matter. Geokhimiya 

Lavrukhina, A.K. 1982. On the nature of isotope anomalies in the early solar system. 

Meteoritika 41:78-9Z 
Levskiy, UK. 1989. Isotopes of inert gases and an isotopicalty hetereogeneous solar system. 

Page 7. In: VIII Nat. Symposium on Stable Isotopes in Geochemistry: Thes. Paper. 

Petaev, M.I., A.K. Lavrukhina, and I.L. Khodakovskiy. 1986. On the genesis of minerals of 

carbonaceous chondrites. Geokhimiya 9:1219-1232. 
Pillinger, C.T. 1984. Light element stable isotopes in meteorites— from grams to picograms. 

Geochim. et Cosmochim. AcU 48(12):2739-2766. 
Shukolyukov, Yu.A. 1988. The solar system's isotopicnonuniformity: principles and conse- 
quences. Geokhimiya 2: 200-211. 
Shulman, L.M. 1987. Comet Nuclei. Nauka, Moscow. 
Voshchinnikov, N.V. 1986. Interstellar dust. Pages 98-202. In: Conclusions of Science and 

Technology. Space research, vol 25. VINITI, Moscow. 

N9 1-2296 6 J 

Magnetohydrodynamic Puzzles in the 
Protoplanetary Nebula 

Eugene H. Levy 
University of Arizona 


Our knowledge of the basic physical processes that governed the 
dynamical state and behavior of the protoplanetary accretion disk remains 
incomplete. Many large-scale astrophysical systems are strongly magnetized 
and exhibit phenomena that are shaped by the dynamical behaviors of 
magnetic fields. Evidence and theoretical ideas point to the possibility that 
the protoplanetary nebula also might have had a strong magnetic field. This 
paper summarizes some of the evidence, some of the ideas, some of the 
implications, and some of the problems raised by the possible existence of 
a nebular magnetic field. The aim of this paper is to provoke consideration 
and speculation, rather than to try to present a balanced, complete analysis 
of all of the possibiUties or to imagine that firm answers are yet in hand. 


Magnetic fields are present and dynamically important in a wide variety 
of astrophysical objects. There are at least three reasons why such magnetic 
fields provoke interest: 1) The presence of a magnetic field invites questions 
as to the conditions of its formation, either as a relict from some earlier 
generation process, carried in and reshaped, or as a product of contempo- 
raneous generation; 2) the Lorentz stresses associated with magnetic fields 
are important to the structure and dynamical evolution of many systems; 
and 3) magnetic fields can store, and quickly release, prodigious quantities 
of energy in explosive flares. The possible presence of a magnetic field in 
the protoplanetary nebula raises questions in all three of these areas. 




Perhaps the most provocative, yet still puzzling and ambiguous, evi- 
dence for strong magnetic fields in the protoplanetaiy nebula comes from 
the remanent magnetization of primitive meteorites. Our ignorance of 
the detailed history of the meteorites themselves, including the processes 
of their accumulation, and ambiguities in the magnetic properties of the 
meteorite material, causes difficulties in interpreting the significance of 
meteorite magnetization. These latter ambiguities are especially confusing 
to neat interpretations of the absolute intensities of the magnetic fields in 
which the meteorites acquired their remanence. A further complication 
arises because the meteorites exhibit a diversity of magnetizations, blocked 
at different temperatures and in different directions on different scales. It 
seems clear that a thorough understanding of meteorite magnetization, and 
its unambiguous interpretation, has yet to be written (Wasilewski 1987). 

A variety of primitive meteorite materials carry remanent magnetiza- 
tion (Suguira and Strangway 1988). Of the wide variety of characteristics of 
meteorite remanence that have been measured, two regularities in partic- 
ular seem to be important. First, the intensities of the remanence-specific 
magnetic moments seem typically to be larger for small components of 
the meteorites (e.g., chondrules and inclusions) than for the aggregate 
rocks. Second, the small, intensely magnetized components are frequently 
disordered and oriented in random directions. 

The inferred model magnetizing intensities for "whole rock" samples 
tend to faU in the range of 0.1—1 Gauss (Nagata and Suguira 1977; Na- 
gata 1979). The connection of this "model" magnetizing intensity to a 
real physical magnetic field depends to some extent on the way in which 
the meteorite accumulated and subsequently evolved in the presence of a 
magnetic field, as well as on the prior magnetic history of the individual 
components. More provocatively, the inferred magnetizing fields for indi- 
vidual small components of meteorites (for example, chondrules) range to 
the order of 10 Gauss (Lanoix et al. 1978; Suguira et al. 1979; Suguira and 
Strangway 1983). Probably even these inferences, although based on mea- 
surements of some of the physically simplest and least heterogeneous of 
meteorite material, shouW be regarded as tentative, pending wider-ranging 
and deeper studies of the processes involved in the acquisition of meteorite 

One interpretation of the measurements is that the meteorite parent 
bodies were assembled out of small components that were already in- 
tensely magnetized as individual, free objects before they were incorporated 
into larger assemblages (Suguira and Strangway 1985). This interpretation, 
while simple and consistent with the measurements, is probably not unique. 


One might imagine, for example, that the randomization of the small com- 
ponents occurred after magnetization, from an internally generated field on 
a larger object, during the subsequent churning of a regolith. However, for 
the present we will accept as a tentative inference that magnetizing fields 
as high as 10 Gauss might have occurred in the protoplanetary nebula. 
Inasmuch as the meteorites seem to have formed at several astronomical 
units, of the order of three, from the Sun, this 10 Gauss magnetic field also 
seems likely to have existed at that distance, although other possibilities 
are not strictly ruled out. 


Assuming the presence of such a nebular magnetic field, there are 
several ways, in principle, that it could have arisen. One possibility is that 
the field could have been generated in the Sun; another possibility is that 
the field could have been a manifestation of the interstellar magnetic field 
compressed by the collapse of the protosolar gas (Safronov and Ruzmaikina 
1985). Consider, however, the possibility that the nebular magnetic field 
was rooted in the early Sun. This possibility is largely attractive in the 
case that the nebula itself was too poor an electrical conductor to have 
its own magnetohydrodynamic character. In that case, the solar magnetic 
field must fall off at least as fast as r~^ in the electrically nonconducting 
space outside of the Sun. (In fact, if there is some ionized gas outflow from 
the Sun, even outside of the disk, the field might fall off somewhat less 
rapidly with distance, but probably not so differently as to alter the general 
conclusion here.) Then for a 10 Gauss magnetic field at 5 x 10" cm from 
a 10" cm radius Sun, the solar surface magnetic field would have had to 
have been about 10^ Gauss. Such a situation would have had a profound 
influence on the Sun, especially with respect to the dynamical equilibrium 
and stability of the system, since the energy associated with such a field 
would have been comparable to the gravitational binding energy of the 
Sun. Clearly, there are many other aspects of this that could be considered. 
However, the purpose here is not to rule out completely the possibility of 
an important nebular field arising from the Sun; rather it is to indicate that 
such an assumption does not lead to an easy and obvious solution of the 
problem of a nebular magnetic field. 

Here we will presume a turbulent nebula in which the short mixing 
times and low electrical conductivity, and the consequent rapid dissipation 
of magnetic fields, quickly erase any memory of the nebular fluid's previous 
magnetization. In this case, if the nebula is to carry a large-scale magnetic 
field, then it must be contemporaneously generated, most likely by some 
sort of dynamo process (Parker 1979; 2:erdovich and Ruzmaikin 1987). 
The possible existence of conditions in the nebula that could have allowed 


the generation of such a magnetic field raises substantial physical questions. 
However, in the spirit of the present discussion, we will assume whatever 
is necessary and come back to the implications in the end. 

The ability of a fluid flow to generate a magnetic field through hy- 
dromagnetic dynamo action can, in simple cases, be parameterized by a 
dimensionless number called the dynamo number, N, where 

N = II^. (1) 

r is a measure of the helical part of the convection while 7 measures 
the strength of the fluid shear, and r/ is the magnetic difTusivity, c^Mtto-, 
with electrical conductivity a; 6 is the scale length of the magnetic field. 
Following a simple analysis for accretion disks (Levy 1978; Levy and Sonett 

T-^-^«|n- (2) 

or r 2 

In a Keplerian disk, n = (GM0/r^)^/^ and to order of magnitude, T «« m, 
where £ is the large scale of the turbulence. Numerically then, 7 ~ 1.7 x 
10i3r-3/2 sec-i and, r ~ 1.1 x lO^^^r-^/^ cm sec-^ Now, taking both the 
scale of the largest eddies, /, and the scale of the magnetic field, 6, to be of 
the order of the scale height of the disk gas, ~ 5 x lO^^ cm, we find that N 
~ 1.3 X 10^^ T]~^, when r ~ 3 AU. Recent detailed numerical calculations 
of magnetic field generation in Keplerian disks indicate (Stepinski and 
Levy 1988) that magnetic field generation occurs at N « 10^. Putting these 
results together, we find that a regenerative dynamo can be expected to 
be effective in such a disk if the electrical conductivity exceeds about 500 
sec~^ We will return to this question in the end. 

Now consider the strength that such a magnetic field might attain. 
Inasmuch as the essential regenerative character of a dynamo fluid motion 
is associated with the cyclonic or helical component of the motion, which 
results from the action of the Q)riolis force, then one estimate of the 
possible maximum amplitude of a dynamo magnetic can be derived from 
balancing the Coriolis force and the Lorentz stress: 

pyn^ ^Y;"" . (3) 


Bp and B^ represent the poloidal and toroidal parts of the magnetic field 
respectively, liking p ~ 10"^ gm cm"^ and V ~ 0.1 kilometers per 
second, then with the other values as above, we find < BpB^ >*/^ ~ 10 
Gauss, as a measure of the maximum magnetic field strength that might 
be produced in such a nebula. Other processes also can act to limit the 


Strength of the magnetic field. For example, with the low ionization level 
indicated above for the action of a nebular dynamo, the strength of the 
magnetic field can be limited by the differential motion of the neutral and 
ionized components of the gas: a phenomenon sometimes called ambipolar 
diffusion. Consideration of this dynamical constraint (Levy 1978) yields a 
limit on the magnetic field strength similar to the one just derived. 

It is provocative that this estimate of the magnetic field strength 
possible in a protoplanetary nebula dynamo agrees so closely with the 
inferred intensity of the magnetizing fields to which primitive meteorites 
were exposed. At this point, the general estimates are sufficiently crude, 
and other questions sufficiently open, that this coincidence probably cannot 
be considered more than provocative. 


One of the most intriguing puzzles posed by meteorites is the evidence 
that some components were exposed to very large and very rapid transient 
excursions away from thermodynamic equilibrium. Specifically, meteorite 
chondrules are millimeter-scale marbles of rock, which apparently were 
quickly melted by having their temperatures transiently raised to some 
17(X)K and then quickly cooled. While there is some uncertainty about 
the time scales involved, the evidence suggests time scales of minutes to 
hours, though some workers have suggested even shorter melting events, 
of the order of seconds. Although a number of possible scenarios have 
been suggested for the chondrule-melting events, none seem to have been 
established in a convincing way (King 1983; Grossman 1988; Levy 1988). 
Here we will focus on the possibility that chondrules melted as a result 
of being exposed to energetic particles from magnetic nebular flares (Levy 
and Araki 1^8). 

In astrophysical systems, explosive restructuring of magnetic fields, 
associated with instabilities that relax the ideal hydromagnetic constraints 
and allow changes in field topology, seems to be among the most prevalent 
of phenomena responsible for energetic transient events. Such events are 
well studied in the Earth's magnetosphere (where they are involved in the 
dissipative interaction between the solar wind and the geomagnetic field and 
in geomagnetic activity) and in the solar corona (where they produce solar 
flares and other transient manifestations). It is thought that many other 
explosive outbursts in cosmical systems result from similar mechanisms. 

lb summarize the analysis given in Levy and Araki (1988), following 
the simple and basic analysis given by Petschek (1964), the energy emerging 
from a flare event is estimated at 



erg cm~^s~^ (4) 


Physically, this corresponds to an energy density equivalent to the energy 
of the magnetic field flowing at the AlMn speed. Levy and Araki conclude 
that, in order to deliver energy to nebular dust accumulations at a rate 
sufficient to melt to the silicate rock, the flares must occur in the disk's 
tenuous corona, with local mass density in the range of 10"^* gm cm~^, 
and with a magnetic field intensity in the range of about 5 Gauss. Under 
these conditions, they estimate that much of the flare energy is likely to 
emerge in the form of 1 MeV particles, which are channeled down along the 
magnetic field; in much the same way that geomagnetic-tail-flare particles 
are channeled to the Earth's auroral ovals. Under these conditions, Levy 
and Araki find that the value to which a particle's temperature can be 
raised is given by 

where To is the ambient temperature into which the particle radiates, and 
which has no substantial influence on the result. From equation (5) it is 
found that the above cited conditions in the flare site, p ~ 10"^* gm cm~^ 
and B ~ 5-7 Gauss, yield flare energy outflows sufficient to melt chondrules; 
substantially weaker magnetic fields or higher ambient mass densities yield 
energy fluxes too low to account for chondrule melting. It is easy to see 
that the time scale constraints for rapid chondrule formation are easily 
met. At the equiUbrium temperature given by equation (5), the rate of 
energy inflow is balanced by radiative energy loss. Thus the heating time 
scale is of the order of the radiative cooling time scale, second to minutes, 
depending on the physical structure of the precursor dust accumulation, 
and the temperature variation of the chondrule closely tracks the variation 
of the energy inflow. 

The conclusion from this exploration is that chondrules might plausibly 
have been melted from magnetic flare energy in the protoplanetary nebula. 
Apparently, the most reasonable conditions under which flares could have 
accomplished this occur for flares in a low-density corona of the disk and 
with magnetic fields having intensities of around 5 Gauss or somewhat 
greater. It is provocative that these conditions are entirely consistent with 
inferences about the possible character of nebular magnetic fields that were 
summarized in the previous two sections. 

If chondrules were made in this way, it is also necessary that the locale 
of chondrule formation was at moderately high altitudes above the nebular 
midplane: below the locale of the flares, but still high enough that the 


matter intervening between the flare site and the chondrule-formation site 
was sufficiently tenuous to allow the passage of MeV protons. This implies 
that the dust accumulations would have to have been melted at an altitude 
of about one astronomical unit above the midplane. It is conceivable that 
dust accumulations might have been melted into chondrules during their 
inward travel from interstellar cloud to the nebula. It is perhaps more likely 
that dust accumulations were lofted from the nebula to high altitudes by gas 
motions. This latter possibility requires that the precursor dust assemblages 
were very loose, flu^, fairy-castle-like structures, somewhat like the dust 
balls that accumulate under beds (Levy and Araki 1988). However, this 
is perhaps the most likely physical state of early dust assemblages in the 
protoplanelary nebula. 

Because the energetic particles associated with the flares described 
here are likely to have had energies in the range of an MeV, it is pos- 
sible that nuclear reactions might also be induced that could account for 
some isotopic anomalies measured in meteorites. However, this possibility 
requires further investigation. 


It is especially instructive to estimate the gross energetics of the flares 
described in the previous section. Again, following Levy and Araki (1988), 
consider that the time scale of the flare is of the order of the heating time 
of the chondrules, somewhere in the range of 10^ to 10^ seconds. Crudely, 
the flare energy is derived from the collapse of a magnetic structure of 
some spatial scale L; in a time tj. The rate of such collapse is expected 
to occur at a fraction of the Alfv6n speed, say ~ 0.1 V^, so that L/ ~ 0.1 
V^ry; the volume of involved magnetic field is then about (0.1 V^r/)^. 
Thus the total flare energy should be of the order of 

Tkking B ~ 5 Gauss and p ~ 10~'* gm cm"^, then cj ranges from some 3 
X 10^" to 3 X 10^® ergs per flare, as the flare time scale ranges from 100 
to 10,000 seconds. For a flare time scale of one hour, equation (6) gives an 
energy of 1.3 x 10^^ ergs. The total flare energy given by equation (6) is 
an especially sensitive function of the magnetic field strength: a 10 Gauss 
magnetic field would multiply all of the above energies by a factor of 32. 

Now it is interesting to compare these results with the observations 
of flaring T TJiuri stars. Such stars show diverse flaring activities over a 
range of time scales and intensities (Kuan 1976). Worden et al. (1981) 
suggest that 10-minute flares on T Tkuri stars release at least 10^ ergs 
per event. This is in the range of flare energies given in the previous 


paragraph. Although there is considerable uncertainty in the numbers and 
in the physical conditions, it is conceivable that at least some of the Hares 
observed on T TJiuri stars are the same phenomenon that we have described 
here as a possible energy source for chondrule melting. 

In a possibly related development, Strelnitskij (1987) has interpreted 
observed linear-polarization rotation angles, in an H2O maser around 
a "young star," to require the presence of an approximately 10 Gauss 
magnetic field at distances of 10 and more astronomical units from the 
central star. It is not clear whether this surprising result has any connection 
to the problems discussed here, but the observation is surely provocative 
in terms of our understanding of the environments of young stars and 


A nebular magnetic field having the strength and distribution discussed 
in this paper would have had substantial effects on the structure and 
dynamical evolution of the system. The main effects would be of two kinds, 
deriving from pressure of the magnetic field and the ability of the field to 
transport angular momentum. 

Consider that a 5 Gauss magnetic field exerts a pressure of just about 
1 dyne/cm^. Compare this with the nebular gas pressure, which, for the 
mass density p ~ 10" ® gm/cm^ and the gas temperature T ~ 300K, is 
about 10 dynes/cm^. Thus the magnetic pressure is about 10% of the gas 
pressure. Although a 10% change in the effective gas pressure seems like 
a relatively small effect, within the context of the ideas discussed here, 
the overall effect of the magnetic field will be, in fact, much larger. The 
magnetic field constitutes a net expansive stress on the system, all of which 
must be confined in equilibrium by the gravity acting on the gas. This 
can be seen in a straightforward way from the magnetohydrodynamic virial 
theorem, lb the extent that the low-mass-density corona also is permeated 
by a significant magnetic field, the expansive stress associated with the 
coronal fields must also be confined by the disk mass. Thus, to make a 
crude estimate, if the volume of coronal space filled with disk-generated 
magnetic field is, say, five times larger than the volume of the disk itself, 
suggested as a possibility in this discussion, then the effective expansive 
stress communicated to the disk gas is some five times larger. In that case 
the magnetic field becomes a major factor in the structure and dynamical 
balance of the disk, especially with respect to the vertical direction. Because 
the magnetic field acts much like a bouyant, zero-mass gas, the dynamical 
behavior of the gas and disk system would be expected to have similarities 
to what we observe in the solar photosphere-corona magnetic coupling. 
This is exactly the situation envisioned above in the speculative picture 


of nebula-corona flares. In that case, the nebula would also be expected 
to exhibit behaviors similar to those described by Parker (1966) for the 
galactic disk. 

The magnetic contribution to angular momentum transport could have 
similarly important effects with a magnetic field such as that considered 
in this paper. Consider the torque transmitted across a cylindrical surface 
aligned with disk axis and cutting the disk at a radius R: 

T^ <Bf^> 2^R\2k), (7) 


where we have included the torque between z = ±A Let ti be the time scale 
for angular momentum transport, then t^ ~ LIT, where L is a characteristic 
angular momentum of the system. Ibking L ~ :rR^(2A)pR^Q we find that 

< BpB^ > 

Taking y/<^^^B^ ~1-10 Gauss results in an evolutionary time scale 
for angular momentum transport of 10^-10'' years. Thus, the presence 
of such a nebular magnetic field would have a substantial impact on the 
angular momentum transport and on the radial evolution of the system. 

This angular momentum transport rate is large in comparison with the 
time scales generally believed to characterize nebular evolution. In that 
respect, it is worth noting effects that could alter the simplest relationships 
between the 1-10 Gauss field strengths and the overall evolution time 
scale. First, we note that MHD dynamo modes in a disk are spatially 
localized (Stepinski and Levy 1988), so that such fast angular momentum 
transport may extend over only limited portions of the nebula at any 
one time. Second, detailed observations of the Sun show us that intense 
magnetic fields may be confined to thin flux ropes, with the intervening field 
strength being much weaker. Such a situation in the nebula, with a spatially 
intermittent magnetic field, might admit the most intense magnetic fields 
inferred from meteorite magnetization, while still producing an overall rate 
of angular momentum transfer much lower than that estimated above. 
Finally, angular momentum transport at the fast rate suggested in the 
previous paragraph might be expected to produce sporadic, temporally 
intermittent evolutionary behavior in the nebula over short time scales. One 
might imagine that the 10^ - lO"* years magnetic timescale could represent 
rapidly fluctuating local weather episodes during the slower, long-term, 
large-scale evolution of the nebula. 



Perhaps the most difficult barrier to understanding the possible pres- 
ence of a substantial magnetic field in the protoplanetary nebula is the 
question of electrical conductivity. Except near its very center, the neb- 
ula was a relatively high-density, dusty gas at relatively low temperatures. 
Under such conditions, the thermally induced ionization fraction and the 
electrical conductivity are very low. Significant levels of electrical conductiv- 
ity require some nonthermal ionization source to produce mobile electrons. 
Consolmagno and Jokipii (1978) point out that ionization resulting from the 
decay of short-lived radioisotopes might have raised the electron fraction to 
the point at which the nebula gas was coupled to the magnetic field. Based 
on their preliminary analysis, Consolmagno and Jokipii suggested that an 
electron density of perhaps a few per cm^ would have been produced with 
the then prevalent ideas about the abundance of ^® Al in the nebula. This is 
sufficient to produce the behaviors described above. Thus, although more 
complete calculations of nebular electrical conductivity are needed (and 
are underway) in light of new information about the cosmic abundance 
of ^®AI (Mahoney et al. 1984) and new information about the dominant 
ion reactions, it is at least possible that the nebula was a sufficiently good 
conductor of electricity to constitute a hydromagnetic system. 


A coherent picture can be drawn of the possible magnetohydrodynamic 
character of the protoplanetary nebula. This picture is based on a mixture 
of evidence and speculation. From this picture emerges a reasonable expla- 
nation of meteorite magnetization, a possible source of transient energetic 
events to account for chondrule formation, a plausible picture of dynamo 
magnetic field generation and field strength in the nebula, and a possible 
connection to energetic outbursts observed in association with protostars. 
This picture has potentially significant implications for our understanding of 
the dynamical behavior and evolution of the protoplanetary nebula because 
a magnetic field having the implied strength and character discussed here 
would have exerted considerable stress on the system. 

The primary unresolved question involves the electrical conductivity of 
the nebular gas. In order for the described picture to be real, the nebular gas 
must conduct electricity well enough to become a hydromagnetic fluid; this 
requires a nonthermal source of ionization. However, other questions also 
press at us. What is the real nature and genesis of meteorite magnetization? 
Are the present, simplest interpretations correct, or is something eluding 
us? Clearly important work remains to be done in this area. What were 
the natures and histories of meteorite parent bodies? Could a magnetizing 


field have been internally generated? We are seriously in need of in situ 
investigation (with sample return) of comets and asteroids. What is the 
nature of protoplanetary environments? Astronomical studies are needed 
to ascertain the small-scale environments associated with star formation 
and protoplanetaiy disks. 

From a broader point of view, it is possible that many things begin to 
fall into place if one presumes that the protoplanetary nebula did, in fact, 
have the characteristics described here. The protosolar system then takes 
on the aspect of a typical astrophysical system, which of course it was, with 
dynamical behaviors thought to be common in many such systems. In this 
case, it seems that a considerable conceptual gap separates the relatively 
simple and well-behaved nebula that emerges from our planetary system- 
based theoretical fantasies, and the energetic, violently active systems that 
we associate with protostars in the astrophysical sky. Some considerable 
work — theoretical, observational, and experimental — remains in order to 
close that gap. 


This work was supported in part by NASA Grant NSG-7419. 


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IV91-22967 t 


Formation of Planetesimals 

Stuart J. Weidenschilling 
Planetary Science Institute 


A widely accepted model for the formation of planetesimals is by 
gravitational instability of a dust layer in the central plane of the solar 
nebula. This mechanism does not eliminate the need for physical sticking 
of particles, despite published claims to that effect. Such a dust layer 
is extremely sensitive to turbulence, which would prevent gravitational 
instability unless coagulation forms bodies large enough to decouple from 
the gas (> meter-sized). Collisional accretion driven by differential motions 
due to gas drag may bypass gravitational instability completely. Previous 
models of coagulation assumed that aggregates were compact bodies with 
uniform density, but it is likely that early stages of grain coagulation 
produced fractal aggregates having densities that decreased with increasing 
size. Fractal structure, even if present only at sub-millimeter size, greatly 
slows the rate of coagulation due to differential settling and delays the 
concentration of solid matter to the central plane. Low-density aggregates 
also maintain higher opacity in the nebula than would result from compact 
particles. The size distribution of planetesimals and the time scale of 
their formation depend on poorly understood parameters, such as sticking 
mechanisms for individual grains, mechanical properties of aggregates, and 
the structure of the solar nebula. 


It is now generally accepted that the terrestrial planets and the cores 
of the giant planets were formed by accretion of smaller solid bodies 


■J _v \ 


(planetesimals). The principal alternative, production of giant protoplanets 
by large-scale gravitational instabilities of the gaseous component of the 
solar nebula, has been abandoned (Cameron 1988). Planetesimals, with 
initial sizes of the order of kilometers, must have formed from much 
smaller particles, perhaps consisting of a mixture of surviving presolar 
grains and condensates from the nebular gas. Such grains were small, 
probably sub-^m in size, and their motions were controlled by the drag of 
the surrounding gas, rather than by gravitational forces. It is necessary to 
understand the aerodynamic processes that affected these small bodies in 
order to understand how planetesimals formed. 

The most common assumption is that planetesimals resulted from 
localized gravitational instabilities within a dust layer in the central plane 
of the nebular disk. Such a layer is assumed to form by settling of grains 
through the quiescent gas due to the vertical component of solar gravity. 
If the dust layer becomes sufficiently thin, and thereby sufficiently dense, it 
is unstable with respect to density perturbations. This instability causes the 
layer to fragment into self -gravitating clumps. These eventually collapse into 
solid bodies, i.e., planetesimals. This process was described qualitatively 
as early as 1949 (Wetherill 1980). Quantitative expressions for the critical 
density and wavelength were derived by Safronov (1969) and independently 
by Goldreich and Ward (1973). The critical density is approximately the 
Roche density at the heliocentric distance a, 

6c ~ 3MQ/27ra^ (1) 

where M© is the solar mass. Perturbations grow in amplitude if they are 
smaller in size than a critical wavelength 

Ae~47^2G'(r,/Q^ (2) 

where cr, is the surface density of the dust layer, G the gravitational 
constant, and Q = (GMQ/a^yf^ is the Kepler frequency. The characteristic 
mass of a condensation is m^ ~ cr,Xc^, and depends only on the two 
parameters a and a. The assumption that a, equals the heavy element 
content of a planet spread over a zone surrounding its orbit (Weidenschilling 
1977a) implies a, ~ lOg cm~^ and m^ ~ lO^^g in the Earth's zone. Density 
perturbations grow rapidly, on the time scale of the orbital period, but 
condensations cannot coUapse directly to solid bodies without first losing 
angular momentum. Goldreich and Ward (1973) estimated the contraction 
time to be ~ 10^ years in Earth's zone, while Pechernikova and Vityazev 
(1988) estimate ~ 10^ - lO^years. 

The assumption that planetesimals formed in this manner has in- 
fluenced the choice of starting conditions for numerical simulations of 
planetary accretion. Many workers (Greenberg et al. 1978; Nakagawa et al. 


1983; Horedt 1985; Spaute et al. 1985; Wetherill and Stewart 1989) have 
assumed an initial swarm of roughly kilometer-sized bodies of uniform size 
or with a narrow size distribution. This assumption was also due to the 
lack of alternative models. 

Another reason for popularity of the gravitational instability model 
was the belief that it requires no mechanism for physical sticking of grains, 
as was explicitly stated by Goldreich and Ward. Because the physical and 
chemical properties of grains in the solar nebula are poorly characterized, 
sticking mechanisms seem ad hoc. Still, there are reasons to believe that 
grains in the solar nebula did experience sticking. It is common experi- 
ence in the laboratory (and Earth's atmosphere) that microscopic particles 
adhere on contact due to electrostatic or surface forces. Weidenschilling 
(1980) argued that for typical relative velocities due to settling in the so- 
lar nebula, van der Waals forces alone would allow aggregates to reach 
centimeter sizes. There are additional arguments that coagulation must 
have produced larger bodies, of meter size or larger, before gravitational 
instability could produce planetesimals. In order to understand these argu- 
ments, it is necessary to review the nature of the aerodynamic interactions 
between solid bodies and gas in the solar nebula. 


We assume that the solar nebula is disk-shaped, has approximately 
Keplerian rotation, and is in hydrostatic equilibrium. If the mass of the 
disk is much less than the solar mass (< O.lMg), then its self-gravity can 
be neglected compared with the vertical component of the Sun's attraction, 
gi = GM0z/a^ = n^z, where z is the distance from the central plane. The 
condition of hydrostatic equilibrium implies that the pressure at z = is 

P, = fiSc/4, (3) 

where E is the surface density of the disk and c is the mean thermal velocity 
of the gas molecules. Equation (3) is strictly true only if the temperature 
is independent of z, but it is a good approximation even if the vertical 
structure is adiabatic. It can be shown that 

P{z) = P,cx^{-z-'/H^), (4) 

where H = 7rc/2fi is the characteristic half-thickness or scale height. 

There is also a radial pressure gradient in the disk. It is plausible 
to assume that the temperature and density decrease with increasing he- 
liocentric distance. Some accretion disk models of the nebula have E 
approximately constant, but equation (3) shows that even these will have a 
strong pressure gradient, because 9. is proportional to a~^/^ for Keplerian 


motion. The decrease in pressure is due primarily to the weakening of 
solar gravity at larger distances. Because the gas is partially supported by 
the pressure gradient in addition to the rotation of the disk, hydrostatic 
equilibrium requires that its velocity be less than Keplerian; 

n 1 a dP 
V^/-n^ + -^. (5) 

where p is the gas density. We define AV = V^ - V^ as the difference 
between the Kepler velocity and the gas velocity. One can show (Weiden- 
schilling, 1977b) that if one assumes a power law for the pressure gradient, 
so that P oc a~", then the fractional deviation of the gas from Vjt is 

where R is the gas constant and /x the molecular weight. We see that 
AVA^i is approximately the ratio of thermal and gravitational potential 
energies of the gas. For most nebular models, this quantity is only a few 
times 10"^, but this is enough to have a significant effect on the dynamics 
of solid bodies embedded in the gas. 


The effects of gas on the motions of solid bodies in the solar nebula 
have been described in detail by Adachi et al. (1976) and Weidenschilling 
(1977b); here we summarize the most important points. The fundamental 
parameter that characterizes a particle is its response time to drag, 

U^mV/Fo, (7) 

where m is the particle mass, V its velocity relative to the gas, and F^ 
is the drag force. The functional form of F^ depends on the Knudsen 
number (ratio of mean free path of gas molecules to particle radius) and 
Reynolds number (ratio of inertial to viscous forces). In the solar nebula, 
the mean free path is typically a few centimeters, so dust particles are in 
the free-molecular regime. In that case, a spherical particle of radius s, 
bulk density p, , has 

'e = sp,/pc. (8) 

The dynamical behavior of a particle depends on the ratio of te to its 
orbital period, or, more precisely, to the inverse of the Kepler frequency. 
A "small" particle, for which Qx^ <C 1, is coupled to the gas, i.e., the drag 
force dominates over solar gravity. It tends to move at the angular velocity 


of the gas. The residual radial component of solar gravity causes inward 
radial drift at a terminal velocity given by 

Vr = -2nAVte. (9) 

Similarly, there is a drift velocity due to the vertical component of solar 

V, = -Q'^zte. (10) 

For a "large" body with Qt„ > 1 gas drag is small compared with solar 
gravity. Such a body pursues a Kepler orbit. Because the gas moves more 
slowly, the body experiences a "headwind" of velocity AV. The drag force 
causes a gradual decay of its orbit at a rate 

Vr = da/dt = -2AV/nt^. (11) 

For plausible nebular parameters, and particle densities of a few g cm"^, 
the transition between "small" and "large" regimes occurs at sizes of the 
order of one meter. The peak radial velocity is equal to AV when nte = 
1. The dependence of a radial and transverse velocities on particle size are 
shown for a typical case in Figure 1. 


Could the gravitational instability mechanism completely eliminate the 
need for particle coagulation? We first consider the case in which there is 
no turbulence in the gas. The time scale for a particle to settle toward the 
central plane of the nebula is r^ = z/V,. From equations (8) and (10), 

n = pc/sp,Q\ (12) 

If we take p ~ IQ-^^g cm"^, n ~ (lO^/s) years, where s is in cm, so 
if s = 1 fim, T^ ~ 10^ years. This is merely the e-folding time for z to 
decrease. For an overall sohds/gas mass ratio f = 3 x 10"^, corresponding 
to the cosmic abundance of metal plus silicates, and an initial scale height 
H ~ c/Q, the dust layer requires ~ 10 r^ ~ 10^ years to become thin 
enough to be gravitationally unstable. This exceeds the probable lifetime 
of a circumstellar disk. Undifferentiated meteorites and interplanetary dust 
particles include sub-^m sized components. These presumably had to be 
incorporated into their parent bodies not as separate grains, but as larger 
aggregates, which settled more rapidly. 

In addition to the problem of settling time scale, there is another 
argument for growth of particles by sticking. A very slight amount of 
turbulence in the gas would suffice to prevent gravitational instability. 


1 1 r 


10* =^AV 


Particle Radius, cm 

FIGURE 1 Radial and transveree velocities relative to the surrounding gas for a spherical 
body with density 1 g/cm^. Also shown is the escape velocity from the body's surface, Ve. 
Numerical values are for the asteroid zone (Weidenschilling 1988) but behavior is similar 
for other parts of the nebula. 

Particles respond to turbulent eddies that have lifetimes longer than ~ tj. 
The largest eddies in a rotating system generally have timescales ~ l/f), so 
bodies that are "small" in the dynamical sense of fite < 1, or less than about 
a meter in size, are coupled to turbulence. A particle would tend to settle 
toward the central plane until systematic settling velocity is of the same 
order as the turbulent velocity, V,. From this condition, we can estimate 
the turbulent velocity that allows the dust layer to reach a particular density 
(Weidenschilling 1988). In order to reach a dust/gas ratio of unity 

Vt ~ f^spjp. 


Typical parameters give V, ~ (sp,) cm sec"^ when s and p, are in cgs units, 
i.e., if particles have density of order unity, then the turbulent velocity of the 
gas must be no greater than about one particle diameter per second in order 


for the space density of solids to exceed that of the gas. In order to reach 
the critical density for gravitational instability, the dust density must exceed 
that of the gas by about two orders of magnitude, with correspondingly 
smaller V(, ~ 10~^ particle diameters per second. For /im-sized grains, 
this would imply turbulent velocities of the order of a few meters per year, 
which seems implausible for any nebular model. 

Even if the nebula as a whole was perfectly laminar, formation of 
a dense layer of particles would create turbulence. If the solids/gas ratio 
exceeds unity, and the particles are strongly coupled to the gas by drag 
forces, then the layer behaves as a unit, with gas and dust tending to 
move at the local Kepler velocity. There is then a velocity difference of 
magnitude AV between the dust layer and the gas on either side. Goldreich 
and Ward (1973) showed that density stratification in the region of shear 
would not suffice to stabilize it, and this boundary layer would be turbulent. 
Weidenschilling (1980) applied a similar analysis to the dust layer itself, 
and showed that the shear would make it turbulent as well. Empirical 
data on turbulence within boundary layers suggest that the eddy velocities 
within the dust layer would be a few percent of the shear velocity Ay or 
several meters per second. The preceding analysis argues that gravitational 
instability would be possible only if the effective particle size were of the 
order of a meter or larger. Bodies of this size must form by coagulation of 
the initial population of small dust grains. 


If it is assumed that particles stick upon contact, then their rate 
of growth can be calculated. The rate of mass gain is proportional to the 
product of the number of particles per unit volume, their masses and relative 
velocities, and some coUisional cross-section. We assume that the latter is 
simply the geometric cross-section, 7r(si + 82)^ (although electrostatic or 
aerodynamic effects may alter this in some cases). For small particles (less 
than a few tens of ^m), thermal motion dominates their relative velocities. 
The mean thermal velocity \sv— (3kT/m)^/^ , where T is the temperature 
and k is Boltzmann's constant. If we assume that all particles have the 
same radius s (a reasonable approximation, as thermal coagulation tends 
to produce a narrow size distribution), the number of particles per unit 
volume is N = 3fp/47rp,s^. The mean particle size increases with time as 

s{t) = «„ + [ibfp {kTlinp]y't\ ' ' (14) 

As a particle grows its thermal motion decreases, while its settling rate 
increases. When settling dominates, a particle may grow by sweeping up 


smaller ones (particles of the same size, or te, have the same settling rate, 
and hence do not collide). If it is much larger than its neighbors, then the 
relative velocity is approximately the settling rate of the larger particle. It 
grows at the rate 


^^fpV./4p,^f^'zs/Ac, (15) 


s{t) = s<,exp {fQ.^zt/4c). (16) 

A particle growing by this mechanism increases in size exponentially on a 
time scale r<, = 4c/iQ^z, or ~ 4/fQ at z ~ c/fi. This time scale is a few 
hundred years at a = 1 AU, and is independent of the particle density or 
the gas density. The lack of dependence on particle density is due to the 
fact that a denser particle settles faster, but has a smaller cross-section, 
and can sweep up fewer grains; the two effects exactly cancel one another. 
Likewise, if the gas density is increased, the settling velocity decreases, 
but the number of accretable particles increases, provided f is constant. 
The time scale increases with heliocentric distance; r^ oc a^/^. A particle 
settling vertically from an initial height Zo and sweeping up all grains that 
it encounters can grow to a size s(max) - {pZo/4ir„ typically a few cm for z^ 
~ c/fi. Actually, vertical settling is accompanied by radial drift, so growth 
to larger sizes is possible. 

The growth rates and settling rates mentioned above have been used 
(with considerable elaboration) to construct numerical models of particle 
evolution in a laminar nebula (Weidenschilling 1980; Nakagawa et al. 1981). 
The disk is divided into a series of discrete levels. In each level the rate of 
collisions between particles of different sizes is evaluated, and the changes 
in the size distribution during a timestep At is computed. Then particles 
are distributed to the next lower level at rates proportional to their settling 
velocities. A typical result of those simulations shows particle growth 
dominated by differential settling. Because the growth rate increases with 
z, large particles form in the higher levels first, and "rain out" toward 
the central plane through the lower levels. The size distribution remains 
broad, with the largest particles much larger than the mean size, justifying 
the assumptions used in deriving equation (16). After ~ 10 r^,, typically a 
few thousand orbital periods, the largest bodies exceed one meter in size 
and the solids/gas ratio in the central plane exceeds unity. The settling 
is non-homologous, with a thin dense layer of large bodies containing ~ 
1-10% of the total surface density of solids, and the rest in the form of 
small aggregates distributed through the thickness of the disk. 

The further evolution of such a model population has not yet been 
calculated. The main difficulty is the change in the nature of the interaction 


between particles and gas when the solids/gas ratio exceeds unity. As 
mentioned previously, the particle layer begins to drag the gas with it. The 
relative velocities due to drag no longer depend only on te, as in equations 
(7-11), but on the local concentration of solids: there is also shear between 
different levels. Work is presently under way to account for these effects, 
at least approximately. A complete treatment may require the use of large 
computers using computational fluid dynamics codes. 


The earlier numerical simulations mentioned above assumed that all 
particles are spherical and have the same density, regardless of size. This is a 
good assumption for coagulation of the liquid drops, but it does not apply to 
solid particles. When two grains stick together, they retain their identities, 
and the combined particle is not spherical. Aggregates containing many 
grains have porous, fluffy structures. It has been shown (Mandelbrot 1982; 
Meakin 1984) that such aggregates have fractal structures. A characteristic 
of fractal aggregates is that the average number of particles found within a 
distance s of any arbitrary point inside the aggregate varies as n(s) <x s^, 
where D is the fractal dimension. The density varies with size according 
to the relation p oc s^~^. "Normal" objects have D = 3 and uniform 
density. Aggregates of particles generally have D ~ 2, so that their density 
varies approximately inversely with size, i.e., they become more porous as 
they grow larger. For the most simple aggregation processes (Jullien and 
Botet 1986; Meakin 1988a,b) the fractal dimension lies in the range 1.7 
< D < 2.2, but more complex mechanisms can lead to values of D lying 
outside of this range. A hierarchical ballistic accretion in which clusters 
of similar size stick at their point of contact yields D < 2. Building up a 
cluster of successive accretion of single grains or small groups, or allowing 
compaction after contact, leads to D > 2. An example of this type is shown 
in Figure 2. This is a computer-generated model, but it corresponds closely 
to soot particles observed in the laboratory (Meakin and Donn 1988). 

The structure of aggregates, which are very unlike uniform-density 
spheres, affects their aerodynamic behavior in the solar nebula. For a 
compact sphere, the response time is proportional to the size (equation 
8). For a fractal aggregate, t^ increases much more slowly with size. 
Meakin has developed computer modeling procedures to determine the 
mean projected area of an aggregate, as viewed from a randomly selected 
direction (Meakin and Donn 1988; Meakin, unpublished). The variation of 
the projected area with the number of grains in the aggregate depends on 
the fractal dimension. If D < 2, aggregates become more open in structure 
at larger sizes, and are asymptotically "transparent," i.e., the ratio of mass 
to projected area never exceeds a certain limit. For D > 2, large aggregates 





S =11186 


FIGURE 2 View of a computer-generated aggregate of fractal dimension ~ 2.11 and 
containing ~ 10'' individual grains. 

are opaque; the mass/area ratio increases without limit, although more 
slowly than for a uniform density object. 

We assume that in the free molecular regime, when aggregates are 
smaller than the mean free path of a gas molecule (> cm in typical nebular 
models), te is proportional to the mass per unit projected area (m/A). From 
the case of a spherical particle in this regime, as in equation (8), we infer 

<e = 5{m/A)/4pc. (17) 

We can express te for aggregates conveniently in terms of the value 


n ( Number of grains per aggregate ) 

FIGURE 3 Mass/area ratio vs. number of grains for aggregates of different dimensions. 
D = 3 assumes coagulation produces a spherical body with the density of the separate 
components (liquid drop coalescence). For D > 2, m/A oc m^~^' , or oc m^'^ for D = 
3, and oc m for D = 2.11. For D < 2, m/A approaches an asymptotic value, shown 

by the arrow. 

for an individual grain, of size s,, and density po, teo = SoPo/pc. Fits to 
Meakin's data give 

te = <e<.(0.343n-°°" + 0.684n-°^^2^ (18) 

for D = 2.11, where n is the number of grains in the aggregate. This relation 
is plotted in Figure 3. For large aggregates of 10^ grains, the mass/area 
ratio and te are ~ 20-30 times smaller than for a compact particle of equal 

Fractal properties of aggregates also have implications for the opacity 
of the solar nebula. The dominant source of opacity is solid grains (Pollack 
et al. 1985). The usual assumption in computing opacity is that particles are 
spherical (Weidenschilling 1984). Their shapes are unimportant if they are 
smaller than the wavelength considered (Rayleigh limit). However, when 
sizes are comparable to the wavelength, the use of Mie scattering theory 
for spherical particles is inappropriate. In the limit of geometrical optics 
when particles are large compared with the wavelength, the opacity varies 
inversely with the mass/area ratio. From Figure 3 we see that if aggregates 
of 10® grains are in the geometrical optics regime, then the opacity is ~ 
20-30 times greater than for compact spherical particles of equal mass. 
Actually, if individual grains are below the Rayleigh limit, aggregates may 
not be in the geometrical optics regime, even if they are larger than the 



wavelength. The optical properties of fractal aggregates need further study, 
but it is apparent that coagulation of grains is less effective for lowering 
the nebula's opacity than has been generally assumed. 


We have modeled numerically the evolution of a population of particles 
in the solar nebula with fractal dimension of 2.11, using the response time 
of equation (18). The modeling program is based on that of Weidenschilling 
(1980). The calculations assumed a laminar nebula with surface density of 
gas 3 X lO^g cm~^, surface density of solids 10 g cm~^ and temperature 
of 500K at a heliocentric distance of 1 AU. At t = the dust was in the form 
of individual grains of diameter l/im, uniformly mixed with the gas. With 
the assumption that coagulation produced spherical particles of dimension 
D = 3, or constant density (the actual value is unimportant; compare the 
discussion of equation (16)), "raining out" with growth of approximately 
10-meter bodies in the central plane occurs in a few times 10^ years. 

For the case of fractal aggregates with D = 2.11, we assumed that 
an individual /im-sized grain (s^ = 0.5 pm) has a density /?<, = 3 g cm"^. 
Aggregates of such grains have densities that decrease with size according 

P, = Po{s/sof-^ (19) 

until s = 0.5 mm, at which size p, ~ 0.01 g cm-^ (densities of this order 
are achieved by some aggregates under terrestrial conditions; Donn and 
Meakin 1988). The density is assumed constant at this value until s = 1 cm, 
and then increases approximately as s^ to a final density of 2 g cm~^ for s 
> 10 cm. This variation is arbitrary, but reflects the plausible assumption 
that fractal structure eventually gives way to uniform density for sufficiently 
large bodies due to collisional compaction. In a laminar nebula, relative 
velocities may be low enough to allow fractal structure at larger sizes than 
assumed here, so this assumption may be conservative. Experimental data 
on the mechanical behavior of fractal aggregates are sorely needed. 

Even the limited range of fractal behavior assumed here has a strong 
effect on the evolution of the particles in the nebula. Growth and settling are 
slowed greatly. After a model time of 2 x 10^ years, the largest aggregates 
are < one millimeter in size. The highest levels of the disk, above one scale 
height, are slightly depleted in solids due to the assumption that the gas 
is laminar. The largest aggregates at this time have settling velocities ~ 1 
cm sec"^ , so there would be no concentration toward the central plane if 
turbulence in the gas exceeded this value. Continuation of this calculation 
results in more rapid growth by differential settling beginning at about 2.5 







1 1 

a = 1 AU 
t = 3 X IO*y 
D= 2.11 



^t = 

= H 

' — 



H . 





10-^ 10"' 

Solids / Gas 


FIGURE 4 Outcome of a numerical simulation of coagulation and settling in the solar 
nebula at a = 1 AU. Aggregates are assumed to have fractal dimension 2.11 at sizes < 
0.1 cm. AT t = 0, dust/gas ratio is uniform at 0.0034, corresponding to cosmic abundance 
of metal and silicates. At t = 3 X 10 y, dust/gas exceeds unity in a narrow region near 
the central plane (expanded scale at right). 

X lO"* years. By 3 x 10^ years there is a high concentration of solids in 
a narrow zone at the central plane of the disk (see Figure 4). This layer 
contains approximately 1% of the total mass of solids, in the form of bodies 
several meters in diameter. 

Evidently, the fractal nature of small aggregates greatly prolongs the 
stage of well-mixed gas and dust, before "rainout" to the central plane. 
The reason for this behavior is subtle, If we assume that the density varies 
as equation (19), then a generalization of the thermal coagulation growth 
rate of equation (14) gives 

s{t) = s,+ {ZD/2 - 2)3/p()bT/27rp3)i/2,3(D-3)/2< 

1 l/(3D/2-2) 


For D = 2.11, this gives s oc t° '*^ vs. s oc t° "* for D = 3. Thus, particle 
sizes increase more rapidly for thermal coagulation of fractal aggregates, 
due to their larger coUisional cross-sections. For aggregates with D > 2, 
the behavior of t^ at large sizes is t^ ~ teo(s/So)°-2. Using this relation 



in equation (15), D appears in both the numerator and denominator, 
leaving the growth rate unchanged. If thermal coagulation is faster for 
fractal aggregates and the growth rate due to settling is independent of D, 
then why is the evolution of the particle population slower? The answer 
is that the derivation of equation (15) assumes that the mass available 
to the larger aggregate is in much smaller particles, so that the relative 
velocity is essentially equal to the larger body's settling rate. Thermal 
coagulation tends to deplete the smallest particles most rapidly, creating 
a narrowly peaked size distribution, and rendering differential settling 
ineffective. Inserting the parameters used in our simulation into equation 
(20) predicts s ~ 0.1 cm at t = 2 x 10^ years, in good agreement with the 
numerical results. 

The qualitative behavior of this simulation, a long period of slow 
coagulation followed by rapid growth and "rainout," is to some degree an 
artifact of our assumption for the variation of particle density with size. A 
transition from fractal behavior to compact bodies without abrupt changes 
in slope would probably yield a more gradual onset of settling. It is likely 
that fractal structure could persist to sizes larger than the one millimeter 
we have assumed here, with correspondingly longer evolution time scales. 

We have not yet modeled the evolution of the particle population after 
the solids/gas ratio exceeds unity in the central plane and can only speculate 
about possible outcomes. At the end of our simulations most of the mass in 
this level is in bodies approximately 10 meters in size. These should undergo 
further collisional growth, and in the absence of turbulence will settle into 
an extremely thin layer. Because these bodies are large enough to be 
nearly decoupled from the gas, it is conceivable that gravitational instability 
could occur in this layer. However, the surface density represented by these 
bodies is small, approximately 1% of the total surface density of solids. 
The critical wavelength, as in equation (2), is correspondingly smaller. If 
they grow to sizes >0.1 km before the critical density is reached, then their 
mean spacing is ~ A,;, and gravitational instability is bypassed completely. 
In any case, the first-formed planetesimals would continue to accrete the 
smaller bodies that rain down to the central plane over a much longer time. 


The settling of small particles to the central plane of the solar nebula is 
very sensitive to the presence of turbulence in the gaseous disk. It appears 
that a particle layer sufficiently dense to become gravitationally unstable 
cannot form unless the particles are large enough to decouple from the gas, 
i.e. > meter-sized. Thus, the simple model of formation of planetesimals 
directly from dust grains is not realistic; there must be an intermediate 
stage of particle coagulation into macroscopic aggregate bodies. 


Coagulation of grains during settling alters the nature of the settling 
process. The central layer of particles forms by the "raining out" of larger 
aggregates that contain only a fraction of the total mass of solids. The 
surface density of this layer varies with time in a manner that depends 
on the nebular structure and particle properties. Thus, if planetesimals 
form by gravitational instability of the particle layer, the scale of insta- 
bilities and masses of planetesimals arc not simply related to the total 
surface density of the nebula. It is possible that collisional coagulation due 
to drag-induced differential motions may be sufficiently rapid to prevent 
gravitational instability from occurring. 

It is probable that dust aggregates in the solar nebula were low-density 
fractal structures. The time scale for settling to the central plane may have 
been one or two orders of magnitude greater than estimates which assumed 
compact particles. The inefficiency of settling by "raining out" suggests that 
a significant fraction of solids remained suspended in the form of small 
particles until the gas was dispersed; the solar nebula probably remained 
highly opaque. The mass of the nebula may have been greater than the 
value represented by the present masses of the planets. 


Research by S.J. Weidenschilling was supported by NASA Contract 
NASW-4305. The Planetary Science Institute is a division of Science 
Applications International Corporation. 


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Horedt, G.P 1985. Icarus 64:448. 

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New York. 
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Spaute, D., B. Lago, and A. Cazenave. 1985. Icarus 64:139. 

Weidenschilling, S.J. 1977a. Astrophys. Space Sci. 51:153. 

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Weidenschilling, S.J. 1988. Pages 348-371. In: Kerridge, J., and M. Matthews, (eds.). 

Meteorites and the Early Solar System. University of Arizona Press, TUcson. 
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Wetherill, G.W., and G. Stewart. 1989. Icarus. 77:330. 


Formation of the Terrestrial Planets from Planetesimals 

George W. Wetherill 
Carnegie Institution of Washington 


Previous work on the formation of the terrestrial planets (e.g. Safronov 
1969; Nakagawa et al. 1983; Wetherill 1980) involved a stage in which on 
a time scale of ~ Vf years, about 1000 embryos of approximately uniform 
size (~ 10^^ g) formed, and then merged on a 10^ - 10* year time scale to 
form the final planets. Numerical simulations of this final merger showed 
that this stage of accumulation was marked by giant impacts (10^^ — 10^* 
g) that could be responsible for providing the angular momentum of the 
Earth-Moon system, removal of Mercury's silicate mantle, and the removal 
of primordial planetary atmospheres (Hartmann and Davis 1975; Cameron 
and \V^rd 1976; Wetherill 1985). Requirements of conservation of angular 
momentum, energy, and mass required that these embryos be confined to 
a narrow zone between about 0.7 and 1.0 AU. Failure of embryos to form 
at 1.5 - 20 AU could be attributed to the longer (~ 10'' years) time scale 
for their initial stage of growth and the opportunity of effects associated 
with the growth of the giant planets to forestall that growth. 

More recent work (Wetherill and Stewart 1988) indicates that the first 
stage of growth of embryos at 1 AU occurs by a rapid runaway on a much 
shorter ~ 3 x 10'' year time scale, as a consequence of dynamical friction, 
whereby equipartition of energy lowers the random velocities and thus 
increases the gravitational cross-section of the larger bodies. Formation of 
embryos at ~ 2 AU would occur in < 10® years, and it is more difficult to 
understand how their growth could be truncated by events in the outer solar 
system alone. Those physical processes included in this earlier work are not 
capable of removing the necessary mass, energy, and angular momentum 




from the region between the Earth and the asteroid belt, at least on such 
a short time scale. 

An investigation has been made of augmentation of outer solar system 
effects by spiral density waves produced by terrestrial planet embryos in 
the presence of nebular gas, as discussed by W^rd (1986). This can cause 
removal of angular momentum and mass from the inner solar system. 
The theoretical numerical coefficients associated with the radial migration 
and eccentricity damping caused by this effect are at present uncertain. 
It is found that large values of these coefficients, compression of the 
planetesimal swarm by density wave drag, followed by resonance effects 
following the formation of Jupiter and Saturn, "clears" the region between 
Earth and the asteroid belt, and also leads to the formation of Earth and 
Venus with approximately their observed sizes and heliocentric distances. 
For smaller, and probably more plausible values of the coefficients, this 
mechanism will not solve the angular-momentum-energy problem. The 
final growth of the Earth on a ~ 10* year time scale is punctuated by giant 
impacts, up to twice the mass of Mars. Smaller bodies similar to Mercury 
and the Moon are vulnerable to collisional fragmentation. Other possibly 
important physical phenomena, such as gravitational resonances between 
the terrestrial planet embryos have not yet been considered. 


This article will describe recent and current development of theories in 
which the terrestrial planets formed by the accumulation of much smaller 
(one- to 10-kilometer diameter) planetesimals. The alternative of forming 
these planets from massive gaseous instabilities in the solar nebula has not 
received much attention during the past decade, has been discussed by 
Cameron et al. (1982), and will not be reviewed here. 

In its qualitative form, the planetesimal, or "meteoric" theory of planet 
formation dates back at least to Chladni (1794) and was supported by 
numerous subsequent workers, among the most prominent of which were 
Chamberlain and Moulton (Chamberlain 1904). Its modern development 
into a quantitative theory began with the work of O.Yu. Schmidt and 
his followers, most notably VS. Safronov. The publication in 1969 of 
his book "Evolutionary of the Protoplanetary Swarm" (Safronov 1969) 
and its publication in English translation in 1972 were milestones in the 
development of this subject, and most work since that time has consisted 
of extension of problems posed in that work. 

The formation of the terrestrial planets from planetesimals can be 
conveniently divided into three stages: 


(1) The formation of the planetesimals themselves from the dust of 
the solar nebula. The current status of this difficult question has been 
reviewed by Weidenschilling et al. (1988). 

(2) The local accumulation of these one- to 10-kilometer planetesi- 
mals into ~ 10^^ - lO^^g "planetary embryos" revolving about the sun in 
orbits of low eccentricity and inclination. Recent work on this problem has 
been summarized by Wetherill (1989a), and will be briefly reviewed in this 

(3) The final merger of these embryos into the planets observed 
today. Fairly recent discussions of this stage of accumulation have been 
given by Wetherill (1986, 1988). This work needs to be updated in order 
to be consistent with progress in our understanding of stage (2). Particular 
attention will be given to that need in the present article. 


The original solid material in the solar nebula was most likely con- 
centrated in the micron size range, either as relic interstellar dust grains, 
as condensates from a cooling solar nebula, or a mixture of these types of 
material. The fundamental problem with the growth of larger bodies from 
such dust grains is their fragility with regard to collisional fragmentation, 
not only at the approximate kilometers per second sound speed velocities 
of a turbulent gaseous nebula, but even at the more modest ~ 60 m/sec 
differential velocities associated with the difference between the gas veloc- 
ity and the Keplerian velocity of a non-turbulent nebula (Whipple 1973; 
Adachi et al. 1976; WeidenschUling 1977). Agglomeration under these con- 
ditions requires processes such as physical "stickiness," the imbedding of 
high-velocity projectiles into porous targets, or physical coherence of splash 
products following impact. Despite serious efforts to experimentally or 
theoretically treat this stage of planetary growth, our poor understanding 
of physical conditions in the solar nebula and other physical properties of 
these primordial aggregates make it very difficult. 

Because of these difficulties, many workers have been attracted to the 
possibility that growth of bodies to one- to 10-kilometer diameters could be 
accomplished by gravitational instabilities in a central dust layer of the solar 
nebula (Edgeworth 1949; Safronov I960; Goldreich and Ward 1973). Once 
bodies reach that size, it is plausible that their subsequent growth would 
be dominated by their gravitational interactions. Weidenschilhng (1984) 
however has pointed out serious difficulties that are likely to preclude the 
development of the necessary high concentration and low relative velocity 
(approximately 10 centimeters per second) in a central dust layer. Therefore 
the question of how the earliest stage of planetesimal growth took place 
remains an open one that requires close attention. 



If somehow the primordial dust grains can agglomerate into one- to 
10-kilometer diameter planetesimals, it is then necessary to understand the 
processes that govern their accumulation into larger bodies. 

The present mass of the terrestrial planets is ~ lO^^g, therefore about 
10^° 10km (~ 10^®g) bodies are required for their formation. It is com- 
pletely out of the question to consider the gravitationally controlled orbital 
evolution of such a large swarm of bodies by either the conventional meth- 
ods of celestial mechanics, or by Monte Carlo approximations to these 
methods. Therefore all workers have in one way or another treated this 
second stage of planetary growth by methods based on gas dynamics, partic- 
ularly by the molecular theory of gases, in which the planetesimals assume 
the role of the molecules in gas dynamics theory. This approach is similar 
to that taken by Chandrasekhar (1942) in stellar dynamics. Nevertheless, 
the fact that the planetesimals are moving in Keplerian orbits rather than 
in free space requires some modification of Chandrasekhar's theory. 

The most simple approach to such a "gas dynamics" theory of plan- 
etesimals is to simply assume that a planetesimal grows in mass (M) by 
sweep up of smaller bodies in accordance with a simple growth equation: 

^ = ^R^p,VF„ (1) 

where R is the physical radius of the growing planetesimal, p, is the 
surface mass density of the material being swept up, V is their relative 
velocity, and F, represents the enhancement of the physical cross-section 
by "gravitational focussing," given in the two-body approximation by 

F, = (l-f25), (2) 

where 9 is the Safronov number, ^ = ^, and V^ is the escape velocity of 
the growing body. 

Although it is possible to gain considerable insight into planetesimal 
growth by simple use of equation (1), its dependence on velocity limits its 
usefuhiess unless a way is found to calculate the relative velocity. Safronov 
(1962) made a major contribution to this problem by recognition that this 
relative velocity is not a free parameter, but is determined by the mass 
distribution of bodies. The mass distribution is in turn determined by the 
growth of the bodies, which in turn is dependent on the relative velocities 
by equation (1). Thus the mass and velocity evolution are coupled. 

Safronov made use of Chandrasekhar's relaxation time theory to de- 
velop expressions for the coupled growth of mass and velocity. He showed 
that a steady-state velocity distribution in the swarm was established as 


a result of the balance between "gravitational stirring" that on the aver- 
age increased the relative velocity, and collisional damping, that decreased 
their relative velocity. The result was that the velocity and mass evolution 
were coupled in such a way that the relative velocity of the bodies was 
self-regulated to remain in the proper range, i.e. neither too high to pre- 
vent growth by fragmentation, nor too low to cause premature isolation 
of the growing bodies as a result of the eccentricity becoming too low. 
In Safronov's work the effect of gas drag on the bodies was not included. 
Hayashi and his coworkers (Nakagawa et al. 1983) complemented the work 
of Safronov and his colleagues by including the effects of gas drag, but 
did not include collisional damping. Despite these differences, their results 
are similar. The growth of the planetesimals to bodies of ~ 10^^ - lO^^g 
begins with a steep initial distribution of bodies of nearly equal mass. With 
the passage of time, the larger bodies of the swarm remain of similar size 
and constitute a "marching front" that diminishes in number as the mass 
of the bodies increases. Masses of ~ l(P®g are achieved in ~ 10® years. 

An alternative mode of growth was proposed by Greenberg et al. 
(1978). They found that instead of the orderly "marching front," runaway 
growth caused a single body to grow to ~ lO^^g in 10* years, at which 
time ahnost all the mass of the system remained in the form of the original 
lO^^g planetesimals. It is now known (Patterson and Spaute 1988) that the 
runaway growth found by Greenberg et al. were the result of an inaccurate 
numerical procedure. Nevertheless, as discussed below, it now appears 
likely that similar runaways are expected when the problem is treated 
using a more complete physical theory and sufficiently accurate numerical 

This recent development emerged from the work of Stewart and Kaula 
(1980) who applied Boltzmann and Fokker-Planck equations to ihe problem 
of the velocity distribution of a swarm of planetesimals, as determined by 
their mutual gravitational and collisional evolution. This work was extended 
by Stewart and Wetherill (1988) to develop equations describing the rate of 
change of the velocity of a body of mass mi and velocity Vi as a result of 
collisional and gravitational interaction with a swarm of bodies with masses 
m2 and vekKities V2. In contrast with earlier work, these equations for the 
gravitational interaaions contain dynamical friction terms of the form 

^ ex im2V,' - m,V,'). (3) 

These terms tend to equipartition energy between the larger and smaller 
members of the swarm. Fbr equal values of Vj and Vj, they cause the 
velocity of a larger mass mi to decrease with time. In earlier work, the 
gravitationally induced "stirring" was always positive-definite, as a result of 
using relaxation time expressions that ensured this result. 


The dV/dt equations of Stewart and Wetherill have been used to de- 
velop a numerical procedure for studying the evolution of the mass and 
velocity distribution of a growing swarm of planetesimals at a given helio- 
centric distance, including gas drag, as well as gravitational and coUisional 
interactions (Wetherill and Stewart 1988). 

When approached in this way it becomes clear that the coupled non- 
linear equations describing the velocity and size distribution of the swarm 
bifuricate into two general types of solutions. The first, orderly growth, was 
described by the Moscow and Kyoto workers. The second is "runaway" 
growth whereby within a local zone of the solar nebula (e.g. 02 AU in width) 
a single body grows much faster than its neighbors and causes the mass 
distribution to become discontinuous at its upper end. Whether or not the 
runaway branch is entered depends on the physical parameters assumed 
for the planetesimals. More important however, are the physical processes 
included in the equations. In particular, inclusion of the equipartition 
of energy terms causes the solutions to enter the runaway branch for a 
very broad range of physical parameters and initial conditions. When 
these ternts are not included, the results of Safronov, Hayashi, and their 
coworkers are confirmed (see Figure 1). On the other hand, when these 
terms are included, runaway solutions represent the normal outcome of the 

The origin of the runaway can be easily understood. For an initial 
swarm of planetesimals of equal or nearly equal mass, the mass distribution 
will quickly disperse as a result of stochastic differences in the collision rate 
and thereby the growth rate of a large number of small bodies. As a result 
of the equipartition of energy terms, this will quickly lead to a velocity 
dispersion, whereby the larger bodies have velocities, relative to a circular 
orbit, significantly lower than that of the more numerous smaller bodies of 
the swarm. The velocity of the smaller bodies is actually accelerated by the 
same equipartition terms that decrease the velocity of the larger bodies. 

A simplified illustration of this effect is shown in Figure 2. This 
calculation is simplified in that effects associated with failure of the two-body 
approximation at low velocities and with fragmentation are not included. 

After only ~ 3 x 10^ years, the velocities of the largest bodies relative 
to those of the smaller bodies has dropped by an order of magnitude. These 
lower velocities increased the gravitational cross-section of the larger bodies 
sufficiently to cause them to grow approximately 100 times larger than those 
bodies in which most of the mass of the swarm is located. This "midpoint 
mass" (mp), defined by being the mass below which half the mass of the 
swarm is located, is indicated on Figure 2. For bodies of this mass the 
Safronov number is 0.6 when defined as 




FIGURE la Evolution of the mass distribution of a swarm of planetesimals distributed 
between 0.99 and 1.01 AU for which the velocity distribution is determined entirely by 
the balance between positive-definite gravitational "pumping up" of velocity and collisional 
damping. The growth is "orderly," i.e., it does not lead to a runaway, but rather to a mass 
distribution In which most of the mass is concentrated in 10 — 10 g bodies at the upper 
end of the mass distribution. 


i.e. its relative velocity is similar to its own escape velocity. In contrast, the 
value of Ol calculated using the velocity of this body and that of the largest 
body of the swarm has a quite high value of 21. 

At this early stage of evolution the growth is still orderly and continuous 
(Figure 3). However, by 1.3 x 10^ years, the velocities of the largest bodies 
have become much lower than their escape velocities (Figure 2), and a 
bulge has developed at the upper end of the swarm as a result of their 
growing much faster than the smaller bodies in the swarm. At 2.6 x 10* 
years, a single discontinuously distributed body with a mass ~ 1(P^ is found. 
At this time it has accumulated 13% of the swarm, and the next largest 
bodies are more than 100 times smaller. This runaway body will quickly 
capture all the residual material in the original accumulation zone, specified 
in this case to be 0.02 AU in width. 

The orbit of the runaway body will be nearly circular, and it will be able 

















V— 5X10* ye.n 










- ^ 

""V^y— IB X lO^yMn 


^vjV__4.0 X 10^ ywrs 





L— 1.0X106v«.n 








1 1 1 1 





,024 ,0^6 lo2« 


FIGURE lb Evolution of the mass distribution of a swarm in which the velocity damping 
is provided by gas drag, rather than by collisional damping. The resulting distribution is 
similar to that of Figure la. 

to capture bodies approaching within several Hill sphere radii (Hill sphere 
radius = distance to colinear Lagrangian points). Even in the absence of 
competitors in neighboring zones, the runaway growth will probably self- 
terminate because additions to its mass (Am) will be proportional to (AD)^, 
where AD is the change in planetesimal diameter, whereas the material 
available to be accumulated will be proportional to AD. Depending on 
the initial surface density, runaway growth of this kind can be expected 
to produce approximately 30 to 200 bodies in the terrestrial planet region 
with sizes ranging from that of the Moon to that of Mars. 

There are a number of important physical processes that have not 
been included in this simplified model. These include the fragmentation of 
the smaller bodies of the swarm, the failure of the two-body approximation 
at low velocities, and the failure of the runaway body to be an effective 
perturber of small bodies that cross the orbit of only one runaway. These 
conditions are more difficult to model, but those calculations that have 
been made indicate that they all operate in the direction of increasing the 
rate of the runaway. 





19 io20 io21 1022 10^3 lO^^ lO^S lO^S 10^^ 

FIGURE 2 Velocity distribution corresponding to inclusion of equipartition of energy 
terms. After 3 X lO"* yeare, the velocities of the largest bodies drop well below that of the 
midpoint mass nip. This leads to a rapid growth of the largest bodies, and ultimately to a 
runaway, as described in the text. 


Because of the depletion of material in their vicinity, it seems most 
likely that the runaway bodies described above will only grow to masses in 
the range of 6 x lO^^g to 6 x lO^^g, and further accumulation of a number 
of these "planetary embryos" will be required to form bodies of the size of 
Earth and Venus. 

Both two-dimensional and three-dimensional numerical simulations 
of this final accumulation of embryos into terrestrial planets have been 
reported. All of these simulations are in some sense "Monte Carlo" cal- 
culations, because even in the less demanding two-dimensional case, a 
complete numerical integration of several hundred bodies for the required 
number of orbital periods is computationally prohibitive. Even if such 
calculations were possible, the intrinsically chaotic nature of orbital evo- 
lution dominated by close encounters causes the final outcome to be so 
exquisitely sensitive to the initial conditions that the final outcome is essen- 
tially stochastic. TWo-dimensional calculations have been reported by Cox 
and Lewis (1980); Wetherill (1980); Lecar and Aarseth (1986); and Ipatov 
(1981a). In some of these two-dimensional cases numerical integration was 
carried out during the close encounter. 




« 10 



" 10^ 



i io< 

I 103 


,7 - 







"^^ 1.3 X 10^B«r» 

_ ^l 







\ ft- 2.6 X 10^ ymn 


\\ 1.3X10Sye»re 

. 1 , 

VJ 2-6 X 10^ yean 

1 1 1 ill ^^ 1 1 


,q18 ,o18 iq20 ,q22 ^g24 .,q 26 ^g^S 

nOURE 3 Effect of introducing equipartilion of energy terms on the mass distribution. 
The tendency toward equipartition of energy results in a velocity dispersion (Figure 2) in 
whidi the velocity (with respect to a dreular orbit) of the massive bodies falls below that 
of the swarm. After ~ 10^ years, a "multiple runaway" appears as a bulge in the mass 
distribution in the mass range 10^'* — lO^^g. After 2.6 X 10^ years, the largest body 
has swept up these larger bodies, leading to a runaway in which the mass distribution is 

discontinuous. The largest body has a mass of 
bodies have masses < 10 g. 


10 g, whereas the other remaining 

The three-dimensional calculations (Wetherill 1978, 1980, 1985, 1986, 
1988) make use of a Monte Carlo technique based on the work of Opik 
(1951) and Arnold (1965). In both the two- and three-dimensional cal- 
culations, the physical processes considered are mutual gravitational per- 
turbations, physical collisions, and mergers, and in some cases collisional 
fragmentations and tidal disruption (Wetherill 1986, 1988). 

In the work cited above it was necessary to initially confine the initial 
swarm to a region smaller than the space presently occupied by the observed 
terrestrial planets. This is necessary because a system of this kind nearly 
conserves mass, energy, and angular momentum. The terrestrial planets 
are so deep in the Sun's gravitational well that very little (< 5%) of the 
material is perturbed into hyperbolic solar system escape orbits. The loss 
of mass, energy, and angular momentum by this route is therefore small. 


Angular momentum is strictly conserved by gravitational perturbations and 
physical collisions. Some energy is radiated away as heat during collision 
and merger of planetesimals. A closed system of bodies, such as a stellar 
accretion disk, that conserves angular momentum and loses energy can 
only spread, not contract. Therefore the initial system of planetesimals 
must occupy a narrower range of heliocentric distance than the range of 
the present terrestrial planets. In particular (Wetherill 1978), it can be 
shown by simple calculations that a swarm that can evolve into the present 
system of the terrestrial planets must be initially confined to a narrow band 
extending from about 0.7 to 1.1 AU. 

In theories in which planetesimals grow into embryos via the orderly 
branch of the bifurcation of the coupled velocity-size distribution equations, 
the time scale for growth of ~ lO^^g embryos at 1 AU is 1 to 2 x 10® years. 
If the surface density of material falls off as a"^/^ beyond 1 AU, the time 
scale for similar growth at larger heliocentric distances will vary as a~^, the 
additional a~^/^ arising from the variation of orbital encounter frequency 
with orbital period. Thus at 2 AU, the comparable time scale for the growth 
of planetesimals into embryos would be 10-20 million years. Jupiter and 
Saturn must have formed while nebular gas was still abundant. Observations 
of pre-main-sequence stars, and theoretical calculations (Lissauer 1987; 
Wetherill 1989b) permits one to plausibly hypothesize that Jupiter and 
Saturn had already formed by the time terrestrial-type "rocky" planetesimals 
formed much beyond 1 AU. In some rather uncertain way it is usually 
supposed that the existence of these giant planets then not only cleared 
out the asteroid belt, aborted the growth of Mars, and also prevented 
the growth of planetesimals into embryos much beyond 1 AU. Interior 
to 0.7 AU, it can be hypothesized that high temperatures associated with 
proximity to the Sun restrained the formation or growth of planetesimals. 

Subject to uncertainties associated with hypotheses of the kind dis- 
cussed above, the published simulations of the final stages of planetaiy 
growth, show that an initial collection of several hundred embryos spon- 
taneously evolve into two to five bodies in the general mass range of the 
present terrestrial planets. In some cases the size and distribution of the 
final bodies resemble rather remarkably those observed in the present solar 
system (Wetherill 1985). The process is highly stochastic, however, and 
more often an unfamiliar assemblage of final planets is found, e.g. ~ three 
bodies, ~ 4 x W'^'^g of mass at 0.55, 1.0, and 1.4 AU. 

Even when the initial embryos are quite small (i.e. as small as 1/6 
lunar mass), it is found that the growth of these bodies into planets is 
characterized by giant impacts at rather high velocities (> 10 kilometers 
per second). In the case of Earth and Venus, these impacting bodies may 
exceed the mass of the present planet Mars. These models of planetary 
accumulation thereby fit in well with theories of the formation of the Moon 


accumulation thereby fit in well with theories of the formation of the Moon 
by "giant splashes" (Hartmann and Davis 1975; Cameron and Ward 1976), 
removal of Earth's atmosphere by giant impacts (Cameron 1983); and 
impact removal of Mercury's silicate mantle (Wetherill 1988; Benz et al. 

Some rethinking of this discussion is required by the results of Wetherill 
and Stewart (1988). Now that it seems more likely that runaway growth 
of embryos at 1 AU took place on a much faster time scale, possibly as 
short as 3 X l(y years, it seems much less plausible that the formation 
of Jupiter and Saturn can explain the absence of one or more Earth-size 
planets beyond 1 AU. Growth rates in the asteroid belt may still be slow 
enough to be controlled by giant planet formation, but this will be more 
difficult interior to 2 AU. 

The studies of terrestrial planet growth discussed earlier in which 
the only physical processes included are collisions and merger, are clearly 
inadequate to cause an extended swarm of embryos to evolve into the 
present compact group of terrestrial planets. Accomplishment of this will 
require inclusion of additional physical processes. 

Three such processes are known, but their significance requires much 
better quantitative evaluation and understanding. These are: 

(1) Loss of total and specific negative gravitational binding energy as 
well as angular momentum by exchange of these quantities to the gaseous 
nebula via spiral density waves (Ward 1986, 1988). 

(2) Loss of material, with its associated energy and angular momen- 
tum from the complex of resonances in the vicinity of 2 AU (Figure 4). All 
of these resonances will not be present until after the formation of Jupiter 
and Saturn, and therefore are not likely to be able to prevent the formation 
of runaway bodies in this region. After approximately one million years 
however, they can facilitate removal of material from this region of the 
solar system by increasing the eccentricity of planetesimals into terrestrial 
planets and Jupiter-crossing orbits. Because bodies with larger semi-major 
axes are more vulnerable to being lost in this way, the effect will be to 
decrease the specific angular momentum of the swarm as well as cause the 
energy of the swarm to become less negative. 

(3) Resonant interactions between the growing embryos. Studies of 
the orbital evolution of Earth-crossing asteroids (Milani et al. 1988) show 
that although the long-term orbital evolution of these bodies is likely to be 
dominated by close planetary encounters, more distant resonant interactions 
are also prominent. Similar phenomena are to be expected during the 
growth of embryos into planets. These have not been considered in a 
detailed way in the context of the mode of planetary growth outlined here, 
but relevant studies of resonant phenomena during planetary growth have 



20 2.5 3:0 3.5 


FIGURE 4 Complex of resonances in the present solar system in the vicinity of 2 AU. 
These resonances are likely responsiUe for forming a chaotic "giant Kirkwood gap" that 
defines the Inner edge of the main asteroid belt. 

been published (Ipatov 1981b; Weidenschilling and Davis 1985; Patterson 

All of these phenomena represent real effects that undoubtedly were 
present in the early solar system and must be taken into consideration in 
any complete theory of terrestrial planet formation. Quantitative evaluation 
of their effect however, is difficult at present, and there is no good reason 
to believe they are adequate to the task. 

A preliminary evaluation of the effect of the first two phenomena, 
spiral densiQr waves and Jupiter-Saturn resonances near 2 AU have been 
carried out Some of the result of this investigation are shown in Figures 5 
and 6. 

In Figure 5 the point marked "initial swarm" corresponds to the 
specific energy and angular momentum of an extended swarm of runaway 
planetesimals extending from 0.45 to 2.35 AU, with a surface density falling 
off as 1/a. The size of the runaway embryos is prescribed by the condition 







"1 — i — I — r 

-| — I — r 

1 — I — I — r 




a-m. '/«». 


L.. -L, J 1 

3.5 4 4.5 5 ,„ 



FIGURE 5 Energy and angular momentum evolution of an initial swarm with runaway 
planetesimal and gas surface density as 1/a between the 0.7 and 2.20 AU. Interior of 0.7 
AU, it is assumed that the gas density is greatly reduced, possibly in an association bipolar 
outflow producing a "hole" in the center of the solar nebula. The surface density falls off 
exponentially between 2.20 and 235 AU and between 0.45 and 0.7 AU. The total initial 
mass of the swarm is 1.407 lO^^g. The open circles represent simulations in which only 
gravitational perturbations and collisional damping are included. The crosses are simulations 
in which mass, angular momentum, and negative energy are lost by means of the resonances 
shown in Figure 3. Tlie solid squares represent simulations in which angular momentum 
and result from inclusion of spiral density wave damping, as described by \%rd (1986, 

that they be separated by 4 Hill sphere radii from one another. As a result, 
the mass of the embryos is 2.3 x 10-^g at 2 AU, 0.8 x lO^^g at 1 AU, 
and 0.5 x 10-''g at 0.7 AU. The specific energy and angular momentum 
of the present solar system is indicated by the point so marked near the 
upper left of the Figure. The question posed here is whether inclusion 
of 2 AU resonances and Ward's equations for changes in semi-major axis 
and eccentricity of the swarm can cause the system to evolve from the 
initial point to the "goal" representing the present solar system. It is found 
that this is possible for sufTicienily large values of the relevant parameters. 
More recent work (Ward, private communication 1989) indicates that the 
published parameters may be an order of magnitude too large. If so, 
this will greatly diminish the importance of this mechanism for angular 
momentum removal. 

The open circles near the initial point show the results of five sim- 
ulations in which neither of these effects were included. Some evolution 
toward the goal is achieved, nevertheless. This results from the more 








(TK •/* 


I I I I I I I I I I I 1 I I I I I I I L-. 





FIGURE 6 Energy and angular momentum loss when both the effects of resonances and 
spiral density are included. For the choice of parameters described in the text, the system 
evolves into a distribution matching that parameters described in the text, the system evolves 
into a distribution matching that observed. 

distant members of extended swarm being more loosely bound than that 
employed in earlier studies, and consequently relatively more loss of bodies 
with higher angular momentum and with less negative energy. 

This effect is enhanced when the resonances shown in Figure 4 are 
included (crosses in Figure 5). The effect of the resonances is introduced 
in a very approximate manner. If after a perturbation, the semi-major axis 
of a body is between 2.0 and 2.1 AU, its eccentricity is assigned a random 
value between 0.2 and 0.8. A similar displacement toward the specific 
angular momentum and energy of the present solar system is reached when 
da/dt and de/dt terms of the form given by Ward (1986, 1988) are included. 
The open squares in Figure 5 result from use of a coefiicient having a value 
of 29 in Ward's equation for da/dt, and a value of 1 for de/dt. The value 
for da/dt is about twice that originally estimated by Ward (1986). 

The effect of including both the resonances and the same values of 
spiral density wave damping are shown in Figure 6. The points lie quite 
near the values found for the terrestrial planets. Thus if one assumes 
appropriate values for these two phenomena, an initial swarm can evolve 
into one with specific energy and angular momentum about that found in 
the present solar system. The initial surface density can be adjusted to 
match the present total mass of the terrestrial planets, without disturbing 
the agreement with the observed energy and angular momentum. Similar 
agreement has been obtained in calculations in which both the gas and 
embryo surface densities varied as a~^/^, instead of a~' as used for the 


data of Figure 6. Satisfactory matching has also been found for a swarm in 
which the gas surface density fell off as a~^/^ whereas the embryo surface 
density decreased as a~^. 

Matching the mass, angular momentum, and energy of the present 
terrestrial planet system is a necessary, but not sufficient condition, for 
a proper model for the formation of the terrestrial planets. It is also 
necessary that to some degree the configuration (i.e. the number, position, 
mass, eccentricity, and inclination) of the bodies resemble those observed. 
Because a model of this kind is highly stochastic, and we have only one 
terrestrial planet system to observe, it is hard to know how exactly the 
configuration should match. As in the earlier work "good" matches are 
sometimes found, more often the total number of final planets with masses 
> 1/4 Earth mass is three, rather than the two observed bodies. It is 
possible this is a stochastic effect, but the author suspects it more likely 
that the differences result from the model being too simple. Neglecting 
such factors as the resonant interactions between the embryos as well as 
less obvious phenomena may be important. 

Like the previous models in which the swarm was initially much more 
localized, the final stage of accumulation of these planets from embryos 
involves giant impacts. Typically, at least one body larger than the present 
planet Mars impacts the simulated "Earth," and impacts twice as large are 
not uncommon. Therefore, all of the effects related to such giant impacts, 
formation of the Moon, fragmentation of smaller planets, and impact 
loss of atmospheres are to be expected for terrestrial planet systems arising 
from the more extended initial embryo swarms of the kind considered here. 
Furthermore, the inward radial migration associated with density wave drag, 
as well as the acceleration in eccentricity caused by the resonances, augment 
the tendency for a widespread provenance of the embryos responsible for 
the chemical composition of the final planets. 


The author wishes to thank W.S. Ward for helpful discussions of 
density wave damping, and Janice Dunlap for assistance in preparing this 
manuscript. This work was supported by NASA grant NSG 7347 and was 
part of a more general program at DTM supported by grant NAGW 398. 


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planetesimals. Pages 355-361. In: Hemenway, C.L., P.M. MiUman, and A.E Cook 

(eds.). Evolutionary and Physical Properties of Meteoroids. AA NASA SP-319. 

N91-22969 ^ 

The Rate of Planet Formation and the 
Solar System's Small Bodies 

Viktor S. Safronov 
Schmidt Institute of the Physics of the Earth 


The evolution of random velocities and the mass distribution of pre- 
planetary body at the early stage of accumulation arc currently under 
review. Arguments have been presented for and against the view of an 
extremely rapid, runaway growth of the largest bodies at this stage with 
parameter values of ^ 10^. DifTiculties are encountered assuming such 
a large 0: (a) bodies of the Jovian zone penetrate the asteroid zone too 
late and do not have time to hinder the formation of a normal-sized planet 
in the astroidal zone and thereby remove a significant portion of the mass 
of solid matter and (b) Uranus and Neptune cannot eject bodies from the 
solar system into the cometary cloud. Therefore, the values < 10^ appear 
to be preferable. 


By the beginning of the twentieth century, Ligondes, Chamberlain, 
and Multan had suggested the idea of planet formation via the combining 
(accumulation) of solid particles and bodies. However, it long remained 
forgotten. It was only by the 1940s that this idea was revived by O.Yu. 
Schmidt, the outstanding Soviet scientist and academician (1944, 1957). He 
initiated a systematic study of this problem and laid the groundwork for 
contemporary planet formation theory. He also suggested the first formula 
for the rate of mass increase of a planet which is absorbing all the bodies 
colliding with it. After it was amended and added to, this formula took on 
its present form (Safronov 1954, 1969): 



dm , /, 2Gm\ 47rr2(T(l + 20) 

— - = xr^pv 1 + — 2— = ^ 

at \ v^r J p 

'^'•Vf 1 + -2- = T -' (1) 

where m and r are the mass and radius of the accreting planet, P is its 
period of revolution around the Sun, p and cr are the volume and surface 
density of solid matter in a planet's zone, and is the dimensionless 
parameter characterizing random velocities of bodies in a planet's zone (in 
relation to the Kepler circular velocity of a preplanetary swarm's rotation): 



oc r0-'/^ (2) 

However, Schmidt did not consider the increase of a planet's collisional 
cross section as a result of focusing orbits via its gravitational field, and the 
factor (1 + 20) in his formula was absent. For an independent feeding 
zone of a planet, the surface density (t at a point in time t is related to the 
initial surface density <To by the simple ratio; 

a = a,{l - m/Q), (3) 

where Q is the total mass of matter in a feeding zone of m. It is proportional 
to the width of the zone 2ARy and is determined, when is on the order 
of several units, by eccentricities of the orbits of bodies, that is, by their 
velocities v; when > 1, it is determined by the radius of the sphere of 
the planet's gravitational influence. In both cases it is proportional to the 
radius of an accreting planet r. (Schmidt took Q to be equal to the present 
mass of a planet.) 

It is clear from (1) and (2) that relative velocities of bodies in the 
planet's zone are the most significant factor determining a planet's growth 
rate. The characteristic accumulation time scale is ra oc 0"^ oc v^. Investi- 
gations have shown that velocities of bodies are dependent primarily upon 
their distribution by mass. Velocities of bodies in the swarm rotating around 
the Sun increase as a result of the gravitational interactions of bodies and 
deaease as a result of their inelastic collisions. In a quasistationary state, 
opposing factors are balanced out and certain velocities are established in 
the system. If the bulk of the mass is concentrated in the larger bodies, 
expression (2) for the velocities is appUcable for velocities with a param- 
eter on the order of several units. In the extreme case of bodies of 
equal mass, « 1. If the bulk of mass is contained in smaller bodies, an 
average gravitating mass is considerably less than the mass m of the largest 
body. The parameter in expression (2) then increases significantly. The 
velocities of bodies, in turn, influence their mass distribution. Therefore, 
we need investigations of the coupled evolution of both distributions to 
produce a strict solution to the problem. This problem cannot be solved 


analytically. We thus divided it into two parts: (1) relative velocities of bod- 
ies were estimated for a pre-assigned mass distribution, and (2) the mass 
spectrum was determined for pre-assigned velocities. At the same time, we 
conducted a qualitative study of the coagulation equation for preplanetary 
bodies. This effort yielded asymptotic solutions in the form of an inverse 
power law with an exponent q: 

n{m) = cm-^, (4) 

(1.5 < q < 2) which is valid for all values m except for the largest bodies. 
Stable and unstable solutions were found and disclosed an instability of 
solutions where q > 2 was noted. In this case, the system does not evolve 
in a steady-state manner. Then the velocities of bodies assumed a power 
the law of mass distribution (3) with q < 2. They are most conveniently 
expressed in the form (2). Then « 3 -^ 5 was found for the system 
without the gas. In the presence of gas, the parameter is two to three 
times greater for relatively small bodies. 

The most lengthy stage was the final stage of accumulation at which 
the amount of matter left unaccreted was significantly reduced. There was 
almost no gas remaining at this stage in the terrestrial planet zone. We 
found from Expression (1) that with = 3 the Earth (<ToW 10 g/cm^) 
accreted about 99% of its present mass in a « 10* year period. The other 
terrestrial planets were also formed during approximately the same time 
scale. The time scale of this accumulation process has been repeatedly 
discussed, revised, and again confirmed for more than 20 years. It may 
seem strange, but this figure remains also the most probable at this time. 

The situation in the region of the giant planets has proven much more 
complex. From eq.(l) we can find an approximate expression for the time 
scale T formation of the planet, assuming a w aoP- Thus, 

where 6 is the planet density. Current masses of the outer planets (Uranus 
and Neptune) correspond to (To « 0.3, that is, to a value about 30 times less 
than in the Earth's zone. The periods of revolution of these planets around 
the Sun P oc R^/^ are two orders of magnitude greater than that of the 
Earth's. Therefore, with the same values for (cited above), the growth 
time scale of Uranus and Neptune would be unacceptably high: T ~ 10" 
years. Of course, this kind of result is not proof that the theory is invalid. 
It does, however, indicate that some important factors have not been taken 
into account in that theory. In order to obtain a reasonable value for T, 
we must increase product Qa„ in (5) several dozen times. More careful 
consideration has shown that such an increase of Qap has real grounds. 


According to (2), velocities of bodies should increase proportionally to 
the radius of the planet. It is easy to estimate that when Uranus and 
Neptune grew to about one half of the Earth's mass (i.e., a few percent of 
their present masses), velocities of bodies for = const ss 5 should have 
already reached the third cosmic velocity, and the bodies would escape the 
solar system. Therefore, further growth of planet mass occurred with v = 
const, and consequently, according to (2), 9 must have increased. With the 
increase of m, the rate of ejection of bodies increased more rapidly than 
the growth rate of the planet, lb the end of accumulation it exceeded the 
latter several times, the parameter begin increased about an order of 
magnitude. It also follows from here that the initial amount of matter in 
the region of the giant planets (that is, a„) was several times greater than 
the amount entered into these planets. Therefore, the difficulty with the 
time scale for the formation of the outer planets proved surmountable (at 
least in the first approximation). Furthermore, the very discovery of this 
difficulty made it possible to discern an important, characteristic feature 
of the giant planet accumulation process: removal of bodies beyond the 
boundaries of the planetary system. Since they are not only removed from 
the solar system, but also to its outer region primarily, a source of bodies 
was thereby discovered which formed the cometary cloud. 

The basic possibility of runaway growth, that is "runaway" in terms of 
the mass of the largest body from the general distribution of the mass of 
the remaining bodies in its feeding zone, has been demonstrated (Safronov 
1%9). Collisional cross-sections of the largest gravitating bodies are pro- 
portional to the fourth degree of their radii. Therefore, the ratio of the 
masses of the first largest body m (planet "embryo") to the mass mi of the 
second largest body, which is located in the feeding zone of m, increases 
with time. An upper limit for this ratio was found for the case of = 
const: lim(m/nii) « (20)^. 

An independent estimate of m/mi based on the present inclinations 
of the planetary rotation axes (naturally considered as the result of large 
bodies falling at the final stage of accumulation) was in agreement with this 
maximum ratio with the values w 3 -^ 5. 

These results were a first approximation and, naturally, required further 
in-depth analysis. Several years later, workers began to critically review the 
results from opposing positions. Levin (1978) drew attention to the fact 
that as a runaway m occurred, parameter must increase. The ratio 
m/mj will correspondingly increase. Assuming mi and not m is an effective 
perturbing body in expression (3), he concluded that the ratio m/mi may 
have unlimited growth. Another conclusion was reached in a model of 
many planet embryos (Safronov and Ruzmaikina 1978; Vityazev et at. 1978; 
Pechemikova and Vityazev 1979). At an early stage all the bodies were 
small. The zones of gravitational influence and feeding of the largest 


bodies, proportional to their radii, were narrow. Each zone had its own 
leader (a potential planet embryo) and there were many such embryos in 
the entire zone of the planet (with the total mass mp): N^ ~ (mp/m)i/^ for 
low values of © and several times greater when 9 was high. Leaders with 
no overlapping feeding zones were in relatively similar conditions. Their 
runaway growth in relation to the remaining bodies in their own zones was 
not runaway in relation to each other. There was only a slight difference 
in growth rates that was related to the change of a/P with the distances 
from the Sun. This difference brought about variation in the masses of 
two adjacent embryos in the terrestrial planet region m/mi ~ 1 + 2m/mp. 
As the leaders grew, their ring zones widened, adjacent zones overlapped, 
adjacent leaders appeared in the same zone and the largest of them began 
to grow faster than the smaller one which had ceased being the leader. 
Masses of the leader grew, but their number was decreased. Normal bodies, 
lagging far behind the leader in terms of mass, and former leaders mi, m2, 
..., the largest of which had masses of ~ 10~^m, were located in the zone 
of each leader m. Consequently, there was no substantial gap in the mass 
distribution of bodies. If the bulk of the mass in this distribution had been 
concentrated in the larger bodies, for example, if it had been compatible 
with the power law (4) with the exponent q < 2, the relative velocities of 
bodies could have been written in the form (2), with values of within the 
first 10. The leaders in this model comprised a fraction //« of all the matter 
in the planet's zone, which for low values of is equal to 

fie - Nem/rrip « {m/mpf^^, (6) 

while for large values of 0, it is several times greater. Approximately 
the same mass is contained in former leaders. At the early stages of 
accumulation m < mp and fte < 1. Thus, velocities of bodies are not 
controlled by leaders and former leaders, but by all the remaining bodies 
and are highly dependent upon the mass distribution of these bodies. In 
the case of the power law (4) with q < 2, runaway embryo growth leads 
only to a moderate increase in to Qmax ~ 10 ^ 20 at Me ~ 10~*, when 
control of velocities begins to be shifted to the embryos and decreases 
to I ^ 2 at the end of accumulation (Safronov 1982). However, it has not 
proven possible, without numerical simulation of the process which takes 
into account main physical factors, to find the mass distribution that is 
established during the accumulation. 

The first model calculation of the coupled evolution of the mass 
and velocity distributions of bodies at the early stage of accumulation 
(Greenberg et al. 1978) ah-eady led to interesting results. The authors 
found that the system, originally consisting of identical, kilometer-sized 
bodies, did not produce a steady-state mass distribution, like the inverse 


power law with q < 2. Only several large bodies with r ~ 200 kilometers had 
formed in it within a brief time scale (210'' years.), while the predominate 
mass of matter continued to be held in small bodies. Therefore, velocities 
of bodies also remained low. Hence, 6 and not v increased in expression 
(2) as m increased. The algorithm did not allow for further extension of the 
calculations. If we approximate the mass distribution contained in Graph 
4 of this paper by the power law (this is possible with r > 5 kilometers), 
we easily find that the indicator q decreases over time from q ^ 10 where 
t = 15,000 years to « 3.5 where t = 22,000 years. It can be expected that 
further evolution of the system leads to q < 2. 

Lissauer (1987) and Artymovich (1987) later considered the possibility 
of rapid protoplanet growth (of the largest body) at very low velocities of 
the surrounding bodies. The basic idea behind their research was the rapid 
accretion by a protoplanet m of bodies in its zone of gravitational influence. 
The width of this zone AR, = kin is equal to several Hills sphere radii 
th = (m/3M0)^/^R. As m increases, zone AR, expands and new bodies 
appear in it, which, according to the hypothesis, had virtually been in 
circular orbits prior to this. According to Artymovich, under the impact of 
perturbations of m, these bodies acquire the same random velocities as the 
remaining bodies of the zone of m over a time scale of approximately 20 
synodical orbital periods. Assuming that any body entering the Hills sphere 
of m, falls onto m (or is forever entrapped in this sphere, for example, 
by a massive atmosphere or satellite swarm, and only then falls onto m), 
Artymovich obtains a very rapid runaway growth of m until the depletion 
of matter in zone AR, within 3 10'' years in Earth's zone and 4 10' years in 
Neptune's zone. Subsequent slow increase of AR, and growth of m occurs 
as a result of the increase in the eccentricity of the orbit of m owing to 
perturbations of adjacent protoplanets. Lissauer estimates the growth rate 
of m using the usual formula (1). Assuming random velocities of bodies 
until their encounters with a protoplanet to be extremely low, he assumes 
that after the encounter they approximate the difference of Kepler circular 
velocities at a distance of AR = Th- That is, they are proportional to 
R~*/^. From this he obtains 0e/ya R. Assuming further that these rates 
are equal to the escape velocity from m at a distance of Th, he finds for R = 
1 AU vfVe = (T/tHy'^ « 1/15, where v. = (2Gm/r)l/^ and he produces the 
"upper limit" of Be// « 400 for this value of vA',. using data from numerical 
integration (Wetherill and Cox 1985). lb generalize the numerical results 
to varying R's, he proposes the expression 

ee/y~400i^ae(^/4)'/^ (7) 

for a "maximum effective accretion cross-section" at the earliest stage of 


accumulation, where Rae denotes the distance from the Sun in astronomical 

This approach has sparked great interest. First of all, it makes it 
possible to reconcile rapid accumulation with runaway of large bodies 
in computations relating to the early stage with slow accumulation in 
computations for the final stage. Runaway growth in the Earth's zone ends 
with m on the order of several lunar masses; in Jupiter's zone it is about 
ten Earth masses (within a time scale of less than 10^ years). Secondly, an 
increase in 6 with a distance oc R from the Sun significantly accelerates the 
growth of giant planets and may help in removing difficulties stemming from 
the length of their formation process. Therefore, we need more detailed 
consideration of the plausibility of the initial assumptions of this work, and 
an assessment of the role of factors which were not taken into account, 
namely, the overlapping of ARj zones of adjacent protoplanets and the 
encounters of bodies with more than one of these and repeated encounters 
of bodies with a protoplanet and collisions between bodies. This would 
allow an estimation of the extent to which the actual values of 6 may differ 
from Lissauer's value for ©e//, qualified by himself as the maximum value. 

The idea of runaway planet growth has not been confirmed in several 
other studies. These include, for example, numerical simulation by Lecar 
and Aarseth (1986), Ipatov (1988), Hayakawa and Mizutani (1988), and 
analytical estimates by Pechernikova and Vityazev (1979). Wetherill notes 
that the runaway growth obtained by Greenberg et al. (1978) is related to 
defects in the computation program. Nevertheless, he feels that runaway 
growth may stem from other, as yet unaccounted factors. The first of these 
is the tendency toward an equiportion of energy of bodies of varying masses, 
which reduces velocity of the largest bodies and leads to acceleration of 
their growth (1990, in this volume). 

Stevenson and Lunine (1988) recently proposed a mechanism for the 
volatile compound enrichment of the Jovian zone (primarily H2O) as a 
result of turbulent transport of volatiles together with solar nebula gas 
from the region of the terrestrial planets. Vapor condensation in the 
narrow band of AR w 0.4 AU at a distance of R w 5 AU may increase 
the surface density of solid matter (primarily ices) in it by an order of 
magnitude and significantly speed up the growth of bodies at an early 
stage. Using Lissauer's model of runaway growth, the authors have found 
a time scale of of ~ 10^ -r 10^ years for Jupiter's formation. 

The possibility of the acceleration of Jupiter's growth by virtue of this 
mechanism is extremely tempting and merits further detailed study. At 
the same time, complications may also arise. If, for example, not one, but 
several large bodies of comparable size are formed in a dense ring, their 
mutual gravitational perturbations will increase velocities of bodies, the ring 
will expand, and accumulation will slow down. In view of this reasoning. 



it must be noted that the question of the role of runaway growth in 
planet formation cannot be considered resolved, despite the great progress 
achieved in accumulation theory. It is, therefore, worthwhile to consider 
how the existence of asteroids and comets constrains the process. 


It is now widely recognized that there have never been normal-sized 
planets in the asteroid zone. Schmidt (1954) was convinced that the growth 
of preplanetary bodies in this zone originally occurred in the same way 
as in other zones, but was interrupted at a rather early stage because 
of its proximity to massive Jupiter. Jupiter had succeeded in growing 
earlier and its gravitational perturbations increased the relative velocities 
of the asteroid bodies. As a result, the process by which bodies merged 
in collisions was superseded by an inverse process: their destruction and 
breakdown. It was later found that Jovian perturbations may increase 
velocities and even expel asteroids from the outermost edge of the belt R 
> 3.5 AU, and resonance asteroids from "Kirkwood gaps," whose periods 
are commensurate with Jupiter's period of revolution around the Sun. The 
gaps are extremely narrow, while the mass of all of the asteroids is only 
one thousandth of the Earth's mass. Therefore, removal of 99.9% of the 
mass of primary matter from the asteroid zone is a more complex problem 
than the increase of relative velocities of the remaining asteroids, (up to 
five kilometers per second, on the average). 

A higher density of solid matter in the Jovian zone, due to condensa- 
tion of volatiles, triggered a more rapid growth of bodies in the zone, and 
correspondingly, the growth of random velocities of bodies and eccentrici- 
ties of their orbits. With masses of the largest bodies > 10^^ g, the smaller 
bodies of the Jovian zone (JZB) began penetrating the asteroid zone (AZ) 
and "sweeping out" all the asteroidal bodies which stood in its way and 
were of significantly smaller size. It has been suggested that the bulk of 
bodies was removed from the asteroid zone in this way (Safronov 1969). 
Subsequent estimates have shown that the JZB could onty have removed 
about one half of the initial mass of AZ matter (Safronov 1979). In 1973, 
Cameron and Pine proposed a resonance mechanism by which resonances 
scan the AZ during the dissipation of gas from solar nebulae. However, it 
was demonstrated (Tbrbett and Smoluchowski 1980) that for this to be true, 
a lost mass of gas must have exceeded the mass of the Sun. In a model of 
low-mass solar nebulae ( ;$, O.IMq), resonance displacement could have 
been more effective as Jupiter's distance from the Sun varied both during 
its accretion of gas and its removal of bodies from the solar system. 

We can make a comparison of the growth rates of asteroids and JZB 
using (1), if we express it as 


dvj {l+2ej)<TjSa\RaJ ' ^' 

where the indices a and j, respectively, denote the zones under consid- 
eration. Assuming Qj « 20a, Sj « 2Sa/% a-j/aa w 3(Rj/Ra)~", that is, 
a threefold density increase in the Jovian zone due to the condensation 
of volatiles, we have drJdTj « (RjfRa)^/'^+"/9 w 0.1 • 2^'^+". It is clear 
from this that the generally accepted value for the density o-g(R) of a 
gaseous solar nebula of n = 3/2 yields dra ss drj, that is, it does not cause 
asteroid growth to lag behind JZB. In order for JZB's to have effectively 
swept bodies out of the AZ, there would have to have been a slower drop 
of (Tg(R) with n » 1/2 (Ruzmaikin et al. 1989) and, correspondingly, for 
solid matter o-j a 15 -h 20 g/cm^. This condition is conserved when there 
is runaway growth of the largest bodies in both zones. Expression (8) 
is now formulated not for the largest, but for the second largest bodies. 
The ratio Qj « 26a is conserved. However, a large body rapidly grows 
in the asteroidal zone, creating the problem of how it is to be removed. 
The second condition for effective AZ purging is the timely appearance 
of JZB's in it Eccentricities of their orbits must increase to 0.3 - 0.4, 
while random velocities of v « ewR must rise to two to three kilometers 
per second. According to (2), the mass of Jupiter's "embryo" must have 
increased to a value of m'j « m^(O.l-0)^/^. It is clear from this that JZB 
penetrating the asteroidal zone at the stage of rapid runaway growth of 
Jupiter's core, according to Lissauer, (with Ge// « 10^ to m^ k ISm^,) is 
ruled out entirely. In view of these considerations, the values of 0j < 20 
-=- 30 and 0a ;$, 10 -=- 15 are more preferable. But the time scale for the 
growth of Jupiter's core to its accretion of gas then reaches 10^ years. 


Large masses of giant planets inevitably lead to high velocities of 
bodies at the final stage of accumulation and, consequently, to the removal 
of bodies from the solar system at this stage. It follows from this that the 
initial mass of solid matter in the region of giant planets was significantly 
greater than the mass which these planets now contain. It also follows that 
part of the ejecta remained on the outskirts of the solar system and formed 
the cloud of comets. The condition, that the totel angular momentum 
of all matter be conserved, imposes a constraint upon the expelled mass 
(~10^m^). Since the overwhelming majority of comets unquestionably 
belongs to the solar system and could not have been captured from outside, 
and since in situ comet formation at distances of more than 100 AU from the 


Sun are only possible with an unacceptably large mass of the solar nebula, 
the removal of bodies by giant planets appears to be a more realistic way 
of forming a comet cloud. The condition for this removal is of the same 
kind as the condition for the ejection of bodies into the asteroidal zone. It 
is more stringent for Jupiter: velocities of bodies must be twice as great. 
For the outer planets, the ejection condition can be expressed as mp/m^ > 
4 (e/Ra«)^/^. It follows from this that Neptune's removal of bodies is only 
possible where < 10^; for Uranus it is only possible for an even lower 0. 


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Hayakawa, M., and H. Mizutani. 1988. Numerical simulation of planetary accretion process. 

Lunar Planet. Sci. XIX:455-456. 
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terrestrial planets. Astrophys. J. 305: 564-579. 
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Astrophysical Dust Grains in Stars, 
the Interstellar Medium, and the Solar System 

Robert D. Gehrz 
University of Minnesota 


Studies of astrophysical dust grains in circumstellar shells, the inter- 
stellar medium (ISM), and the solar system, may provide information about 
stellar evolution and about physical conditions in the primitive solar nebula. 
Infrared observations give information about the mineral composition and 
size distribution of the grains. Grain materials identified in sources exter- 
nal to the solar system include silicates, siUcon carbide, amorphous carbon, 
and possibly hydrocarbon compounds. The nucleation and growth of as- 
trophj^ical carbon grains has been documented by infrared observations of 
classical novae. In the solar system, dust is known to be a major constituent 
of comet nuclei, and infrared spectroscopy of comets during perihelion 
passage has shown that the ablated material contains silicates, amorphous 
carbon, and hydrocarbons. Cometary grains resemble extra-solar-system 
grains in some ways, but there is evidence for additional processing of the 
grain materials in comets. Comets are discussed as a possible source for 
zodiacal dust 

Solar system grain materials have been sampled by the collection 
of micrometeorites and by isolating microscopic inclusions in meteorites. 
Meteorite inclusions exhibit several chemical abundance anomalies that are 
similar to those predicted to be produced in the explosive nucleosynthesis 
that accompanies novae and supemovae. The possible connections between 
extra-solar-system astrophysical dust grains and the grains in the solar 
system are explored. A recent suggestion that grains are rapidly destroyed 
in the interstellar medium by supernova shocks is discussed. Experiments to 
establish the relationships between extra-solar-system astrophysical grains 




and solar system grains, and between cometary dust and the zodiacal dust 
are suggested. Among the most promising are sample return missions and 
improved high-resolution infrared spectroscopic information. 


Small refractory dust grains are present in circumstellar shells around 
many different classes of stars, in the interstellar medium (ISM), and in 
comets and the zodiacal cloud in the solar system. The mineral composition 
and size distribution of the grains in all three environments have similarities, 
but there are also distinct differences. Condensable elements produced in 
stars during nucleosynthesis presumably condense into grains during the 
final mass-loss stages of stellar evolution in aging stars Uke M-type giants 
and supergiants (Gehrz 1989), or during nova and supernova eruptions 
(Clayton 1982; Gehrz 1988). These grains can be expelled into the ISM 
where they may be processed further by supernova shocks and in molecular 
clouds. The grains can eventually be incorporated into young stars and 
planetary systems during star formation in the clouds (Gehrz et al. 1984). 

Dusty and rocky solids that may derive from remnants of the forma- 
tive phase are present in our own solar system and around some other 
main-sequence stars. Grains could therefore be a significant reservoir for 
condensable elements, effecting the transportation of these elements from 
their sites of production in stars into new stellar and planetary systems. 

Studies of astrophysical grains can provide significant information 
about stellar evolution, physical conditions in circumstellar environments, 
and processes that occur during star formation. In particular, grains in 
the solar system may contain evidence about conditions in the early solar 
nebula. A major issue is whether grains made by stars actually survive 
intact in significant quantities as constituents of mature planetary systems, 
or whether most of the dust we see in the ISM and the solar system 
represents a re-accretion of condensables following the destruction of cir- 
cumstellar or interstellar grains. There is theoretical evidence that grains 
can be destroyed in both the ISM (Scab 1987) and during the formation 
of planetaiy systems (Boss 1988). A paucity of gas-phase condensables in 
the ISM (Jenkins 1987), a low input rate to the ISM of dust from evolved 
stars (Gehrz 1989), and evidence for a hydrocarbon component in ISM 
grains (Allamandola et al. 1987) all suggest that grains can accrete material 
in molecular clouds. If the grains can survive the interstellar and star for- 
mation environments intact, then studies of the elemental abundances and 
minerology of solar system grains may provide fundamental information 
about stellar nucleosynthesis and evolution. If the grains are substantially 
processed, or evaporate and recondense after leaving the circumstellar 


environment, then their chemical history may be much more difficult to 
evaluate, and their current composition may reflect relatively recent events. 
This review discusses the observed characteristics of astrophysical grains, 
compares the properties of grains in the solar and extra-solar environments, 
and suggests investigations to address the question of whether Stardust is 
an important constituent of solar system solids. 


Infrared observations made more than two decades ago provided the 
first convincing evidence that dust grains are present in the winds of late- 
type giant and supergiant stars. Most of this circumstellar dust is refractory 
material. Woolf and Ney (1969) were the first to recognize that silicate 
grains, similar in mineral composition to materials in the Earth's crust and 
mantle, were a major constituent of the dust in oxygen-rich stars. 

Circumstellar Stardust around carbon-rich stars is composed primarily 
of amorphous carbon and silicon carbide (Gehrz 1989). The identification 
of the silicate and SiC material comes from 10 and lOfxm emission features 
caused by the Si-O/Si-C stretching and O-Si-O bending molecular vibra- 
tional modes (see Figures 1 and 2). Silicates, having the triatomic molecule 
Si02 in their structure, show both the features. The diatomic molecule SiC 
cannot bend, and therefore exhibits only the fitn stretching feature. The 
10 and 20/im emission features in stellar objects are broad and generally 
devoid of the structure generally diagnostic of crystaline silicate minerals 
like Olivine and Enstatite (Rose 1979; Campins and Tbkunaga 1987). This 
suggests that the silicateous minerals in Stardust are amorphous, and that 
the grains probabty have a considerable spread in size distribution. 

Some astrophysical sources exhibit near infrared emission or absorp- 
tion features in the 3.1 to 3.4/im spectral region (see Figure 3) that have 
been attributed to stretching vibrations in C-H molecular bonds associ- 
ated with various hydrocarbon compounds (Allamandola 1984; Sakata et 
al. 1984; Allamandola et al. 1987; Allen and Wickramasinghe 1987). The 
hydrocarbon grain materials proposed to account for these features in- 
clude polycyclic aromatic hydrocarbons (PAH's), hydrogenated amorphous 
carbon (HAC's), and quenched carbonaceous composites (QCC's). There 
is evidence for the presence of hydrocarbon grains in the near infrared 
spectra of a handful of stellar objects (see de Muizon et al. 1986; Gehrz 

Observations have confirmed the existence of dust in circumstellar 
environments other than those associated with late-type stars. Dust is 
known to have condensed around novae (Gehrz 1988) and probably can 





^ 10^ 






<^ 10^ 

III i ir I I L 

3.6 4.9 

8 7 10,0 II 4 12.6 




RU Vir 


.—— N 

LW Ser / X 




-X X 

•-• \-x 



SgrA o 



03 05 1.0 

3,0 5.0 10,0 



FIGURE 1 The infrared energy distributions of various objects that show emission or 
absorption due lo small astrophysical dust grains. VY CMa and /i Cep are M supergiants 
(oxygen-rich stars) that have strong 10 and 20fj.m silicate emission features (Gehrz 1972). 
Tticse same emission features appear in the comae of comets (Comet Kohouiek) where the 
grains are small (Ney 1974). The superheat in the coma dust continuum shows that the 
grains, probably amorphous carbon, producing this continuum are also small. The feature is 
weak in the Kouhoutek antilail because the grains are large (Ney 1974). General interstellar 
silicate absorption at 10 and 20/im is evident in the nonthermal spectrum of the Galactic 
Center source Sgr A (data from Hackwell et at. 1970). Carbon stars (RU Vir) often show 
a 11.3/im emission feature caused by SiC and a near infrared thermal continuum due to 
amorphous carbon (Gehra et al. 1984). Novae (LW Ser) form carbon dust in their ejecta 
(Gehrz et al. 1980). The carbon produces a grey, featureless continuum from 2 to 23/zm. 
The superficial similarities in the spectra of these objects is striking. 


form in the ejecta from supernovae, though there is as yet no unambigu- 
ous observational evidence for supernova dust formation (Gehrz and Ney 

A small amount of dust is also present in the winds of planetary nebulae 
(Gehrz 1989) and Wolf-Rayet (WR) stars (HackwcU et al. 1979, Gehrz 
1989). The Infrared Astronomical Satellite (IRAS) provided far infrared 
data that show evidence for the existence of faint, extended circumstellar 
dust shells around some main sequence (MS) stars (Aumann et al. 1984; 
Paresce and Burrows 1987). These shells, typified by those discovered 
around Vega (a Lyr) and /? Pic, are disk-like structures believed to be fossil 
remnants of the star formation process. Although the material detected 
by IRAS around MS stars is most likely in the form of small and large 
grains, the presence of planets within the disks cannot be ruled out. The 
existing data are not spatially or spectrally detailed enough to lead to 
definitive conclusions about the mineral composition and size distribution 
of these fossil remnants of star/planetary system formation. There are large 
amounts of dust present in the circumstellar regions of many young stellar 
objects (YSO's), often confined in disk-like structures that are associated 
with strong bipolar outflows (Lada 1985). In the case of YSO's, it is unclear 
whether the dust is condensing in the wind or remains from the material 
involved in the collapse phase. 

Most main-sequence stars and older YSO's do not have strong infrared 
excesses from dust shells, nor do they show evidence for visible extinction 
that would be associated with such shells. It is tempting to conclude that 
the shells in these objects have been cleared away in the early stages of 
stellar evolution by stellar winds, by Poynting-Robertson drag, or by the 
rapid formation of planets (see the contribution by Strom et al. in these 
proceedings). Rapid clearing of the circumstellar material poses a problem 
for the rather long time scale apparently required for the formation of 
giant planets (see the contribution by Stevenson in these proceedings). An 
alternative possibility is that dust grains grow to submillimeter or centimeter 
sizes (radii from 100 microns to 10 centimeters) during the contraction 
of the core to the Zero Age Main Sequence (ZAMS). Such grains will 
produce negligible extinction and thermal emission compared to an equal 
mass of the 0.1-10 micron grains that are believed to make up most of 
the material in circumstellar shells that reradiate a substantial fraction of 
the energy released by the central star. It can be shown that the opacity 
of a circumstellar shell of mass M = N4fl-pa^/3 (where N is the number 
of grains in the shell, p is the grain density, and a is the grain radius) is 

SN 1987a is believed to have condensed dusl grains about 400 days after its eruption. TTie dust 
formation is discussed in an analysis of recent infrared data by R.D. Gehrz and E.P. Ney (1990. 
Proc. Natl. Acad. Sci. 87:4354-4357). 




4 6 8 10 12' 14 


FIGURE 2 High-resolulion infrared spectra of Ihe 7-14 micron emission and absorption 
features of different astrophysical sources illustrating some basic differences between exlra- 
solar-system sources and comets. The classical astrophysical 10/im silicate emission feature, 
typified by the "B-apezium emissivity profile (Gilletl et al 1975) and the M-supergianl BI 
Cyg (Gehrz et al 1984), peaks at 9.7/im. It is broad and without structure, suggesting 
that the grains are amorphous with a wide range of grain sizes. The feature appears 
in absorption in compact sources deeply embedded in molecular cloud cores such as the 
BN (Becklin-Neugebauer) object in Orion (Gillett et al. 1975). The carbon star RU Vir 
exhibits a classical 11.3/im SiC emission feature (Gehrz et al. 1984). Comet Kohoutek 
data are from Merrill (1974) as presented by Rose (1979). The 10// emission feature of 
Kohoutec is similar to the classical astrophysical silicate feature. P/Haney-s emission feature 
(Bregman et al 1987) shows detailed structure suggesting that the grain mixture contains 
significant quantities of ciystaline anhydrous silicate minerals. The solid line to the P/Halley 
data is a fit based on spectra of IDP's with Olivene and Pyroxene being the dominant 
components (Sandford and Walker 1985). The feature at 6.8//m may be due to carbonates 
or hydrocarbons. 


inversely proportional to the grain radius if M is held constant A shell 
of 0.1 micron grains would be reduced in opacity by a factor of 10^ if the 
grains were accreted into 10 cm planetesimals while the total circumstellar 
dust mass remains constant. A 10 L© star would require the age of the 
solar system to clear 10 cm planetesimals from a circumstellar radius of 
10 AU by Poynting-Robertson drag, and the sweeping effects of radiation 
pressure on 10 cm grains would be negligible. It would appear possible 
to postulate scenarios for the accretion of large circumstellar bodies that 
are consistent with both the relatively rapid disappearance of observable 
circumstellar infrared emission and the long time scales required for giant 
planet formation. 


The observations described above suggest that many classes of evolved 
stellar objects are undergoing steady-state mass loss that injects Stardust 
of various compositions into the interstellar medium. Gehrz (1989) has 
estimated the rates at which various grain materials are ejected into the 
ISM by different classes of stars. Stardust formation in most stars is a 
steady-state process, and the detailed physics of the grain formation is 
exceedingly difficult to resolve with current observational capabilities. In- 
frared studies of objects exhibiting outbursts that lead to transient episodes 
of dust formation, on the other hand, have revealed much about the for- 
mation of Stardust and its ejection into the ISM. The long-term infrared 
temporal development of a single outburst is governed by the evolution of 
the grains in the outflow. Observations have shown that it is possible in 
principle to determine when and under what conditions the grains nucleate, 
to follow the condensation process as grains grow to large sizes, to record 
the conditions when grain growth ceases, and to observe behavior of the 
grains as the outflow carries them into the ISM. 

The primaiy examples of transient circumstellar dust formation have 
been recorded in classical nova systems (Gehrz 1988) and WR Stars (Hack- 
well et al. 1979). In both cases, grains nucleate and grow on a time scale of 
100 to 200 days, and the grains are carried into the ISM in the high-velocity 
outflow. The dust formation episodes apparently occur as frequently as ev- 
eiy five years in WR stars and about once per 100-10,000 years in classical 
novae. About 10"^ to 10""^ solar masses of dust form in each episode, and 
the grains can grow as large as 0.1 to 0.3 microns. There is evidence that the 
grains formed in nova ejecta are evaporated or sputtered to much smaller 
sizes before they eventually reach the ISM. Novae have been observed 
to produce o^^gen silicates, silicon carbide (SiC), amorphous carbon, and 
perhaps hydrocarbons (Gehrz 1988; Hyland and MacGregor 1989); WR 
stars apparently condense iron or amorphous carbon (Hackwell et al. 1979). 






9 10 












^ 8 








IRS 7 



3.0 3.2 3.4 3.6 3.8 


FIGURE 3 High-resolution infrared spectra of the 3.3-3.4/i hydrocarbon emission and 
absorption bands in three cxlra-solar-syslems sources and Comet Halley. The Orion Bar 
is a shocked emission region in a molecular cloud; the Orion Bar curve is drawn after 
data from Brcgman et al. (1986, in preparation) as shown in Figure 1 of AUamandola et 
al (1987). IRAS 21282+5050 is a compact star-like object of undetermined nature (after 
data from de Muizon et al. 1986). Comet P/Hallcy (Knacke et al. 1986) has features that 
are broader and peak at longer wavelengths than the features of the comparison objects. 
Bottom curve shows a 3.5/im interstellar absorption feature in the spectrum of IRS 7, a 
highly reddened source near the Galactic Center (Jones et al. 1983). 


Classical novae typify the episodic circumstellar dust formation process. 
Their infrared temporal development progresses in several identifiable 
stages. The initial eruption results from a thermonuclear runaway on the 
surface of a white dwarf that has been accreting matter from a companion 
star in a close blnaiy system. Hot gas expelled in the explosion is initially 
seen as an expanding pseudophotosphere, or "fireball." Free-free and 
line emission are observed when the expanding fireball becomes optically 
thin. A dust condensation phase, characterized by rising infrared emission, 
occurs in many novae within 50 to 200 days following the eruption. The 
infrared emission continues to rise as the grains grow to a maximum radius. 
Grain growth is terminated by decreasing density in the expanding shell. 
The Infrared emission then declines as the mature grains are dispersed by 
the outflow into the ISM. The rate of decline of the infrared radiation and 
the temporal development of the grain temperature suggest that the grain 
radius decreases either by evaporation or sputtering during their dispersal. 
Existing observations are consistent with the hypothesis that the nova grains 
could be processed to interstellar grain sizes before they reach the ISM. 

Hydrocarbon molecules described above (PAH's, HAC's, QCC's) may 
produce some of the infrared emission features observed in planetary neb- 
ulae, comets, and molecular cloud cores (see Figure 3 and Allamandola et 
cd. 1987). Although Hyland and MacGregor (1989) have reported possible 
hydrocarbon emission from a recent nova, and Gerbault and Goebel (1989) 
have argued that hydrocarbons may produce anomalous infrared emission 
from some carbon stars, there is currently no compelling evidence that 
hydrocarbon grains are an abundant constituent of the dust that is expelled 
into the ISM in stellar outflows (Gehrz 1989). Generally, circumstellar 
hydrocarbon emission is observed only in sources with high-excitation neb- 
ular conditions (Gehrz 1989). There is circumstantial evidence that grains 
condensed in the ejecta of novae, supernovae, and WR stars may contain 
chemical abundance anomalies similar to those in solar system meteorite 
inclusions (see below and Clayton 1982; Tl^uran 1985; Gehrz 1988). 


Hackwell et cd. (1970) showed that the same 10- and 20-meter silicate 
features responsible for emission in M-stars were present in absorption in 
the infrared spectrum of the non-thermal Galactic Center source Sgr A. 
They concluded that the absorption was caused by interstellar silicate grains 
in the general ISM and that the grains are similar to those seen in M-stars. 
Interstellar silicate absorption has since been confirmed for a variety of 
other objects that are obscured by either interstellar dust or cold dust in 
molecular clouds (see, for example, the BN object in Figure 2 and the other 
objects embedded in compact HII regions discussed by Gillett et al. 1975). 


There is roughly 0.04 mag of silicate absorption per magnitude of visual 
extinction to Sgr A. Observations of stellar sources with interstellar silicate 
absorption along other lines of sight in the Galaxy yield similar results. 

Continuum reddening by interstellar dust in the general ISM has been 
measured by a number of investigators who compared optical/infrared 
colors of reddened luminous stars with the intrinsic colors exhibited by 
their unreddened counterparts (Sneden et al. 1978; Rieke and Lebofslg^ 
1985). Interstellar dust also polarizes starlight (Serkowski et al. 1975). 
An estimate of the grain size distribution for the grains causing this so- 
called "general" interstellar extinction can be made given the wavelength 
dependence of the reddening and polarization curves. The same reddening 
and polarization laws appear to hold in all directions in the galaxy that 
are not selectively affected by extinction by dense molecular clouds. The 
reddening and polarization curves observed for stars deeply embedded in 
dark and bright molecular clouds lead to the conclusion that the grains in 
clouds are substantially larger than those causing the general interstellar 
extinction (Breger et al. 1981). 

The shape of the general interstellar extinction curve as determined 
by optical/infrared measurements is consistent with the assumption that 
the ISM contains carbon grains of very small radii (0.01-0.03/im) and a 
silicate grain component (Mathis et al. 1977; Willner 1984; Draine 1985). 
Both components are also observed in emission in dense molecular cloud 
cores where the dust is heated by radiation from embedded luminous 
young stars (Gehrz et al. 1984). The ISM dust in dense clouds contains a 
probable hydrocarbon grain component that causes the 3.2-3.4/im emission 
features (see Figure 3), and several other "unidentified" infrared emission 
features that are seen in the 6-14/im thermal infrared spectra of some 
HII regions, molecular cloud cores, and young stellar objects (Allamandola 
1984; Allamandola et al. 1987). Jones et al. (1983) showed that a 3.4/im C-H 
stretch absorption feature is present in the spectrum of the highly reddened 
source IRS7 towards the Galactic Center (see Figure 3). SiC has not been 
observed in either the general extinction or in the extinction/emission by 
molecular ctoud grains, but its presence may be obscured by the strong 
silicate features. 

At least some of the dust present in the ISM must be Stardust produced 
by the processes described above. Gehrz (1989) has reviewed the probable 
sources for the production of the dust that is observed to permeate the 
ISM. These include condensation in winds of evolved stars, condensation 
in ejecta from nova and supernovae, and accretion in dark clouds. Most 
of the silicates come from M stars and radio luminous OH/IR (RLOH/IR) 
stars; carbon stars produce the carbon and SiC. Some stars, novae, and su- 
pernovae may eject dust with chemical anomalies. Since there is apparently 


not a substantial stellar source of hydrocarbon grains, the ISM hydrocar- 
bon component may be produced during grain processing or growth in 
molecular clouds. The observation that there are large grains in molecular 
clouds provides additional evidence that grains can grow efficiently in these 


The thermal infrared energy distributions of the comae and dust tails 
of most comets (see Figures 1 and 2) show the characteristic near infrared 
continuum dust emission that is probably caused by small iron or carbon 
grains, and prominent 10 and 20m emission features characteristic of silicate 
grains (Ney 1974; Gehrz and Ney 1986). The cometary silicate features, first 
discovered in Comet Bennett by Maas et al. (1970), suggest that comets 
contain silicate materials similar to those observed in the circumstellar 
shells of stars and in the ISM. Determinations of the composition of 
Halley's coma grains by the Giotto PIA/PUMA mass spectrometers appear 
to confirm the silicate grain hypothesis (Kissell et al. 1986). There are some 
basic differences however, between the cometary 10m emission features 
and their stellar/interstellar counterparts (see Figure 2). As discussed 
above, the latter are broad and structureless suggesting a range of sizes 
and an amorphous grain structure. The lO^m feature in P/Halley, on the 
other hand, shows definite structure that suggests the presence of a grain 
mixture containing 90% crystalline silicates (55% olivines, 35% pyroxene) 
and only 10% lattice-layer silicates (Sandford and Walker 1985; Sandford 
1987; Gehrz and Manner 1987). This observation would imply that the 
grains in some comets may have undergone considerable high-temperature 
processing compared to extra-solar-system grains. Some pristine comets, 
like Kohoutek, show a 10m feature more like the stellar feature (see 
Figure 2 and Rose 1979). In the case of Kohoutek, the model fits indicate 
that the mineral composition is almost entirely low- temperature hydrated 
amorphous silicates (Rose 1979; Campins and Tbkunaga 1987; Manner and 
Gehrz 1987; Brownlee 1987; and Sanford 1987). 

The 3 to 8^m thermal continuum radiation in the comae and Type II 
dust tails of most comets are often hotter than the blackbody temperature 
for the comet's heliocentric distance (Ney 1982). This "superheat" suggests 
that the grains are smaller than about 1 micron in radius. ISM grains may 
be 10 to 100 times smaller than this. The antitail of Kohoutek was cold 
with only weak silicate emission showing that comets also have much larger 
grains frozen in their nuclei (Ney 1974). 

The 3.3-3.4/im feature (see Figure 3) in P/Halley suggests the presence 
of hydrocarbon grains in the ablated material. It is obvious that the Halley 
emission feature differs substantially both in width and effective wavelength 


from the 3.3-3.4^m emission seen In other astrophysical sources. The 
implication is that the material in P/Halley has been processed in some way 
compared with the material observed in extra-solar-system objects. 

Comets are presumably a Rosetta Stone for the formation of the 
solar system because the contents of their nuclei were frozen in the very 
early stages of the accretion of the solar nebula. The grains contained 
therein may be indicative of interstellar material in the primitive solar 
system, or may represent material processed significantly during the early 
collapse of the solar system. These materials are ablated from comet 
nuclei during perihelion passage. Cometary particles injected into the 
interplanetary medium by ablation probably produce the shower meteors 
and the zodiacal cloud. Studies of zodiacal dust particles may therefore 
provide important information about the properties of cometary dust grains. 
No cometary or zodiacal particles have yet been collected in situ. However, 
Brownlee (1978) and his recent collaborators have collected grains believed 
to be interplanetary dust particles (IDP's) from the stratosphere, on the 
Greenland glaciers, and off the ocean floor. These particles yield infrared 
absorption spectra showing that they are composed primarily of crystalline 
pyroxene and olivines, and layer-lattice silicates (Sandford and Walker 
1985). Composite spectra modeled by combinations of these particles 
have been shown to match the Halley and Kohoutek data reasonably well 
(Sandford and \\^lker 1985; Sandford 1987). There is no evidence for 
3.4/im hydrocarbon features in the laboratory spectra of IDP's, but there 
are spectral pecularities that are associated with carbonaceous minerals. 
Wilker (198"^ has analyzed the minerology of IDP's and concludes that 
they are comprised largely of materials that were formed in the solar system 
and contain only a small fraction of ISM material in the form of very small 
grains. The comparisons between IDP's and comets are, of course, only 
circumstantial at present. It is therefore crucial to contemplate experiments 
to collect zodiacal particles and cometary grains to establish the connections 
between zodiacal, cometary, and interstellar/circumstellar particles. 


An intriguing question is whether significant numbers of Stardust grains 
can survive from the time that they condense in circumstellar outflows 
until they are accreted into the cold solid bodies in primitive planetary 
systems. While there is evidence that grains are rapidly destroyed in the 
ISM by supernova shocks (Seab 1987) and are heated above the melting 
point in the nebular phases of collapsing stellar systems (Boss 1988), there 
is equally compelling evidence for the existence of solar-system grains 
that are probably unaltered today from when they condensed long ago 
in circumstellar outflows (Clayton 1982). If Stardust cannot survive long 


outside the circumstellar environment, then most of the grains in evolved 
planetary systems must be those that grew in ISM molecular clouds and/or 
those that condensed in the collapsing stellar systems. 

It is difficult to escape the conclusion that grains can be destroyed 
in the ISM. Seab (1987) has reviewed the possibility that ISM grains are 
rapidly destroyed by supernova shock waves on veiy short time scales (1.7-5 
X 10^ yrs). He notes however, that the extreme depletion of refractory 
grain materials in the ISM is difficult to reconcile with the destruction 
hypothesis. Assuming the gas mass in the Galactic ISM is 5 x 10® M© with 
a gas to dust ratio of 100/1, shocks will process 10-30 Mq yr~^ in gas and 
destroy 0.1-0.3 Mq yr~' in dust. 

Despite the rapid destruction that may befall ISM grains, it appears 
likely that they can reform and grow to large sizes in molecular clouds and 
star formation regions. Gehrz (1989) examined the galactic dust ecology by 
comparing circumstellar dust injection with depletion by star formation and 
supernova shocks and found that dust grains may be produced by accretion 
in molecular clouds at one to five times the circumstellar production rate. 
There is currently no observational evidence for a substantia] stellar source 
of hydrocarbon grains. If this is the case, then the production of hydro- 
carbon grains and hydrocarbon mantles on Stardust may be primarily an 
ISM process. Seab (1987) has predicted rapid accretion rates for grains in 
molecular clouds («10^ — 10^ years) which implies that such clouds could 
be efficient sources for the production and/or growth of dust in the ISM. 
Depletions in the ISM of heavy elements associated with dust (Jenkins 
1987) are a strong indication that any gas-phase heavy elements ejected 
from stars are efficiently condensed onto ISM dust grains. Since early-type 
stars (WR stars, Of stars), and supernovae can eject a significant amount 
of gas-phase condensable matter on a galactic scale, it seems highly likely 
that these materials must be incorporated into dust in the ISM itself. 

There is substantial evidence that there were high temperatures (1700- 
2000K) in the early solar nebula within a few AU of the sun (Boss 1988) 
so that most small refractory grains in this region would have melted 
or vaporized. On the other hand, microscopic inclusions in solar system 
meteorites exhibit abundance anomalies that may have been produced by 
the condensation of grain materials in the immediate vicinity of sources of 
explosive nucleosynthesis such as novae or supernovae (Clayton 1982). For 
example, ^^Ne can be made by the reaction ^^Na(/?+'')^^Ne which has a 
half-life of only 2.7 years, so that ^^Ne now found in meteorite inclusions 
(the so-called Ne-E anomalie) must have been frozen into grains shortly 
after the production of ^^Na in a nova eruption (Tturan 1985). Another 
anomaly seen in meteorite inclusions that can be produced in nova grains 
is excess "Mg from ^^ Al(p+''f ^Mg which has a half-life of 7.3 x 10^ 
years. Infrared observations have now revealed several novae in which 


forbidden fine structure line emission has provided evidence for chemical 
abundance anomaUes that would be associated with the production of ^^Na 
and 2®A1 (Gehrz 1988). Xe can be produced by a modified r-process in 
nucleosynthesis supernovae and trapped in grains that condense in the 
ejecta (Black 1975). Some of these anomalies also imply that the grains 
survived intact from their sites of circumstellar condensation until their 
accretion into the body of the meteorite. High-temperature processing 
might be expected to drive off volatiles such as ^^Ne and Xe which are 
highly overabundant in some inclusions. 


The investigation of the properties of astrophysical dust grains is an 
area that can benefit from studies that use the techniques of both astro- 
physics and planetary science. It is now possible to conduct both remote 
sensing and in situ experiments to determine with certainty the mineral 
composition and size distribution of the dust in the solar system. The Vega 
and Giotto flybys of Comet P/Halley produced some tantalizing results that 
demand confirmation. A sample return mission to a comet or asteroid is 
of the highest priority. Any mission that returns a package to Earth after 
a substantial voyage through the solar system should contain experiments 
to collect interplanetary dust particles. It will be important to establish 
whether IDP's that are collected from space resemble those collected on 
the Earth and whether they have chemical anomalies that are similar to 
those seen in meteorite inclusions. Examples of missions now planned that 
could be modified to include IDP dust collection are Comet Rendezvous 
and Asteroid Flyby (CRAF) and the MARS SAMPLE RETURN missions. 
The mineral composition of the zodiacal cloud remains uncertain. Infrared 
satellite experiments to measure the spectrum of the cloud can provide sig- 
nificant diagnostic information. Near infrared reflectance spectroscopy can 
reveal the presence, mineral composition, and size distribution of various 
types of silicate grains. These features have already been observed in the 
spectra of asteroids. Emission spectroscopy can determine whether silicates 
and silicon carbide are present. The contrast of the W-lOfna emission fea- 
tures are related to the size distribution (Rose 1979). Ground-based studies 
of the mineralogy of Stardust and solar system dust also require high signal 
to noise high-resolution spectroscopy of the emission features shown in 
Figures 1 and 3 in a wide variety of sources. New improvements in infrared 
area detectors should make achievement of this objective realistic within 
the coming decade. 



The author is supported by the National Science Foundation, Na- 
tional Aeronautics and Space Administration, the U.S. Air Force, and the 
Graduate School of the University of Minnesota. 


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Late Stages of Accumulation and 
Early Evolution of the Planets 


Schmidt Institute of the Physics of the Earth 


This article briefly discusses recently developed solutions of problems 
that were traditionally considered fundamental in classical solar system 
cosmogony: determination of planetary orbit distribution patterns, values 
for mean eccentricity and orbital inclinations of the planets, and rotation 
periods and rotation axis inclinations of the planets. We will examine 
two important cosmochemical aspects of accumulation: the time scale 
for gas loss from the terrestrial planet zone, and the composition of the 
planets in terms of isotope data. We conclude that the early beginning of 
planet differentiation is a function of the heating of protoplanets during 
collisions with large (thousands of kilometers) bodies. This paper considers 
energetics, heat mass transfer processes, and characteristic time scales of 
these processes at the early stage of planet evolution. 


Using the theory of preplanetary cloud evolution and planet forma- 
tion, which is based on the ideas of Schmidt, Gurevich, and Lebedinskiy, 
and which was developed in the works of Safronov (1969, 1982), we can 
estimate a number of significant parameters for the dynamics of bodies 
which accumulate in the planets. However, it long proved impossible to 
solve a number of problems in classical solar system cosmogony which 
were traditionally considered fundamental. Such problems include the the- 
oretical derivation of patterns of planetary and satellite orbit distributions 
(the so-called Titius-Bode law), theoretical estimations of the value for 



mean orbital eccentricities and inclinations, planet rotation periods and 
rotation axis inclinations, and other characteristics of the present structure 
of the Sun's planetary system. In addition, certain consequences of the 
theory and, most importantly, a conclusion on the relatively cold initial 
Earth and the late beginning of its evolution, clashed with data on geo- 
and cosmochemistry. These data are evidence of the existence of planet 
heating during the process of growth and very early differentiation. This 
paper briefly discusses a modified version of the theory which the authors 
developed in the 1970's and 1980's. Using this new version we were able 
to provide a fundamental solution to several key problems of planetary 
cosmogony and generate a number of new findings. The most significant 
of these appear to be an estimate of the composition of an accumulating 
Earth with data incorporated on oxygen isotopy and a conclusion on the 
early beginning of differentiation in growing planets. 


Despite promising data on the existence of circumstellar disks, we 
have yet to discover an analogue to a circumsolar gas-dust disk. Nor 
have calculations (Ruzmaikina and Maeva 1986; Cassen and Summers 
1983) produced a satisfactory picture of circumsolar disk formation, or a 
reliable estimate of its mass M and characteristic initial dimensions R*. 
Nevertheless, a model of a low-mass disk (M < 0.1 M©), with moderate 
turbulence, a hot circumsolar zone and cold periphery, has received the 
widest recognition in the works of a majority of authors. 


A reconstruction of surface density distribution (t(R) according to 
Weidenshilling (1977) is shown in Figure 1. Mass of the disk, generated by 
adding on to produce the cosmic (solar) composition of present-day planet 
matter, is 

(0.01 - 0.07)Mo,with (r{R > R„ = lAU) « {RjRo)-^!^. 

It is usually supposed that by the time the Sun achieved main sequence, 
its luminosity L, did not greatly differ from the present L©, and the 
temperature in the disk's central plane (z = 0) was on the order of a 
black body T ~ 300(Ro/R)'''^K. Estimations of the degree of ionization 
(Ne/N ~ 10-^^) and gas conductivity ( < lO^CGSE) in the central plane 
are insignificant, and the impact of the magnetic field is usually neglected 
in considering subsequent disk evolution. Using the hydrostatic equations 



FIGURE 1 Surface density distribution a(R) in low-mass, circumstellar gaseous disks. 
The solid line indicates models of disks near F5 class stars: 1: m/k = 1; 2: m/k = 1/2; 
3: m/k = 1/4; the dashed line indicates models of disks near GO class stars: 4: m/k = 1 
5: m/k =1/2; 6: m/k =1/4; the dotted and dashed line shows disks near G5 class stars: 7 
m/k = 1; 8: mA = 1/2; 9: m/k = 1/4; the straight lines are critical density distributions for 
the corresponding classes of stars: 10: <7cr(F5); 11: a„(GOy, 12: <Tcr(G5). Disk mass in 
models 1-12 is equal to M - 510 ~'^Mq. 13 is the standard model. 


and the equation of the state of ideal gas at a temperature which is not 
dependent on z, we yield a density distribution for z: 

p{z) w po{R)txp(-zyh^), K^ = 2kTR^/GMQfi, (1) 

where ^(w 2.3) is the mean molecular mass, and k is the Boltsman constant. 
The model which has been termed standard is derived, by taking into 
account a(R) ~ >/? p<,(R)h(R): 

PoiR) oc R°-^,P{R) oc R-^,T{R) oc R-'',a < l,/?~ 3. (2) 

Flattening of the disk is high: j = h/R oc (RT)^f^, j < 0.1. Disk rotation 
is differential and differs little from Kepler's: 

« = wi(l + iy/\ wk = Vt/R = ^GMq/R^, (3) 

( « (c^/^t^)(d In P/d In R) < 0.1, c^ = kT/^l. 

Here c, is the speed of sound. In the standard model V^^ > c,^ > 
v^^, v^ is the Alfven velocity. Quasiequilibrium disk models are constructed 
by Vityazev and Pechernikova (1982) which do not use the contemporary 
distribution (t(R). They were called MK-models since they are only defined 
by a mass M and a moment K of a disk which is rotating around a star with 
mass M, and luminosity L». Expressions for densities p(R,z) and a(R) were 
obtained by resolving the system of hydrodynamic equations with additional 
conditions (low level of viscous impulse transport and minimum level of 
dissipative function). The distribution of surface density in disks was found 
to be: 

.(«)., .55.10>^(f)"(^)'"' 

«-exp[-2.8(f)'(^)%Wcm'. (4) 

where M is iTilO~^M$, K is klO^^g cm's"^ and R is in AU. By varying 
m and k, star mass M,, and luminosity L,, we can generate a set of 
modek of quasiequilibrium circumstellar disks (see Figure 1). We will 
note that the distributions of a (R) in the standard and MK-models are 
qualitatively similar. However, there is a noticeable excess of matter in 
the remote zone in the first model in comparison to the latter ones. This 
excess may be related to diffusion spread of the planetesimal swarm during 
planet accumulation. Therefore, present planetary system dimensions may 



FIGURE 2 Evolution of Ihe preplanetaty disk. The left side shows flattening of the 
dust subdisk and the formation of the swann of planelesimals. The right side illustrates 
plantesimals joining together to form planets (Levin 1964). 

primary stages of its evolution and of planet formation (Figure 2) within 
the framework of the aforementioned low-mass disk models. 


After dust settles on the central plane and dust clusters are formed 
due to gravitational instability, there occurs the growth and compacting of 
some clusters, and the breakdown and absorption of others. This process 
is described in detail by Pechernikova and Vityazev (1988). We later briefly 
touch upon the specific features of the final stages of accumulation of 
sufficiently large bodies, when a stabilization effect develops for the orbits 
of the largest bodies (Vityazev et al. 1990). In the coagulation equation 


dn{m,t) ^1 r j^^^i,n_^i)riim')n(m-m')dm'-n{m,t) 
2 ^0 


/ A'""{m,m')n{m')dTn\ (5) 



the subintegral kernel A(ni,m"), describing collision efficiency, must take 
into account the less efficient difTusion of large bodies. Let us write 
ACm.m") = A*B/(A* + B), where 

A' = ri(r + r'f[l + 2G{m + m»)/(r + r')V'']V = Vi^Vi,, 

is the usual coefficient which characterizes the collision frequency of gravi- 
tating bodies m and m" with good mixing, 

B = [D{m) + £»(m'')][Ai?(m) + ARim")] = D^ARit, 

is the coefficient accounting for diffusion, D(m) = e^(m)R^/r£(m), e is the 
eccentricity, te is the characteristic Chandrasekhar relaxation time scale, 
AR = eR. Estimates demonstrate that at the initial stages (m < 0.1 m^) B 
> A* and A — > A*, while at the later stages (m > 0.1m®) we have B(i ~ 
k) < A*(i ~ k) and in the limit A(i ~ k) — B(i ~ k). Pechernikova (1987) 
showed that if A oc (m" + m'") = m,*" then the coagulation formula has 
an asymptotic solution that can be expressed as 

n{m) oc m~' ,q= 1 + a/2. (6) 

For the initial stages a = 2/3 - 4/3 and q, = 4/3 - 5/3. For the later stages 
B(i ~ k) a m.jfc-^/^ and q* ~ 1/6, q* < q < q,, that is, the gently sloping 
power law spectrum for large bodies. With this finding we can understand 
the relative regularity of mass distribution in the planetary system. Unlike 
the findings of numerical experiments (Isaacman and Sagan 1977), only the 
low mass in the asteroid belt and a small Mars is an example of significant 
fluctuation. The authors, using numerical integration of equations, such as 

-1 5 .„ ,3d 
'''' = -RdR^'^'^''''^+RdR 


also examined the overall process of solid matter surface density redistri- 
bution (Ti(R,l) {(Ti ~ 10~^<t) resulting from planctesimal diffusion. The 
spread effect of a disk of preplanet bodies proved significant for the later 
stages and was primarily manifested for the outer areas (Vityazev et al. 
1990). The effect is less appreciable for the zone of the terrestrial planet 
group, and we shall forego detailed discussion of it here. 


Wetherill's numerical calculations for the terrestrial planet zone (1980) 
confirmed the order of value of relative velocities that had been estimated 
earlier by Safronov (1969). Similar calculations for the zone of outer planets 


are preliminary. In particular, there is vagueness in the growth time scales 
for the outer planets. By simplifying the problem for an analytical approach, 
we can look separately at the problem of mean relative velocities iJ (i.e. e, 
I) of the planetesimals and the problem of eccentricities e and inclination 
1 of the orbits of accreting planets. The second problem is considered 
below. We will discuss here an effect which is important in the area of 
giant planets. As planetesimal masses (m) grow, their relative velocities (v) 
also increases. At a sufficiently high mean relative velocity (tJ ~ 1/3 ■ Vt) 
part of the bodies from the "high velocity Maxwell tail" may depart the 
system, carrying away a certain amount of energy and momentum. With 
this scenario, the formula for the mean relative velocity (Vityazev et al. 
1990; Safronov 1969) must appear as follows: 

t)2 dt te Tg r, ' 

where te, Tg and r, are correspondingly the characteristic Chandrasekhar 
relaxation time scales, gas deceleration and the characteristic time scale 
between collisions, ftl = 0.05-0.13 (Safronov 1969; Stewart and Kaula 
1980), P2 = 0.5 (Safronov 1969) and ue is part of the amount of energy 
removed by the "rapid particles" 

1 r°° f^ 

i/£W-/ vMv)dv/ v^n{v)dv = r{b/2,b)/6rib/2)K (9) 
6 ./„„ Jo 

For now e ~ i ~ vA^t < 1, the usual expressions for v follow from (8), in 
particular, with Tg:s> te, ts in a system of bodies of equal mass m we have 

V = ^Gm/Qr,^heTe ~ 1. (10) 

Despite continuing growth of the mass, as e approaches &„ « 0.3 - 0.4, ue 
becomes comparable to /?i, the relative velocity ? in the system of remaining 
bodies discontinues growth. In other words, with e ss e^r, the parameter 
6 in expression (10) grows with m proportionally to m^/^, reaching in the 
outer zone values ~ 10^. This effect gives us acceptable time scales for 
outer planet growth. Because of low surface density, accreting planets in 
the terrestrial group zone cannot attain a mass sufficient with a build up of 
e to &„• Therefore the mean eccentricities do not exceed the values 6^01 
= 0.2 - 0.25. 



Studies on accumulation theory previously assumed that in terms of 
mass a significant runaway of planet embiyos from the remaining bodies 
in the future planet's feeding zone occured at an extremely early stage. 
According to Safronov's well-known estimates (1969), the mass of the 
largest body (after the embryo) mi was 10~^-10~^ of the mass m of the 
accreting planet. Pechemikova and Vityazev (1979) proposed a model for 
expanding and overlapping feeding zones, and they considered growth of 
the largest bodies. The half-width of a body's feeding zone is determined 
by mean eccentricity e of orbits of the bulk of bodies at a given distance 
from the Sun: 

AR{t) ~ e{t)R ~ v{t)RjVk, (11) 

The characteristic mixing time scale for R in this zone virtually coincides 
with the characteristic time scale for the transfer of regular energy motion 
to chaotic energy motion, and the characteristic time scale for energy 
exchange between bodies. It is clear from (10) and (11) that 

v{t) oc r{t),e{t) oc r{t),AR{t) oc r{t). (12) 

The mass of matter in the expanding feeding zone 

Q{R,t)^2w ajRdR, (13) 


will also grow with a time scale <x r(t), while disregarding the difference in 
matter diffusion fluxes across zone boundaries. When the mass of a larger 
body m(t) begins to equal an appreciable amount Q(t) with the flow of 
time (see Figure 3), the growth of the feeding zone decelerates. At this 
stage the larger bodies of bordering zones begin to leave behind, in terms 
of their mass, the remaining bodies in their zones. However, (as seen in 
Figure 3), this runaway by mass is much less than was supposed in earlier 


Mass increase of the largest body in a feeding zone is represented by 
the well-known formula: 

dm/dt = 7rr2(l + 20)pdV = 2(1 -|- 2e)r'^Wk(Td, (14) 

where the surface density of condensed matter o-j can be considered a 
sufficiently smooth function R and it can be assumed that <Td(t=0) = 




0.01 005 

I I I 


0.5 0.6 0.7 0.8 0.9 m/M® 


0.1 0.2 0.3 0.4 







FIGURE 3 The region of determination and model distributions for m\lm as the ratio 
of the mass, mj , of the largest body in the feeding zone of a growing planet to the mass 
of a planet m: 1: mi/m = 1 - 0.62 (m/Q)°^, which corresponds to the growth of bodies 
in the expanding feeding zone; 1: m2An; 3: ma/m; 4: mi/m = 1 - m/Q; 5: mi/m = (1 - 
m/Q)^. The circles and dots indicate the results of numerical simulation of the process of 
terrestrial planet accumulation (Ipatov 1987; Wetherill 1985). 


(To(R„fR)'' with its values <To and v in each zone. As bodies precipitate 
to the largest body in a given zone m, a growing portion of matter is 
concentrated in m and the corresponding decrease in surface density is 
written as: 

<Td(0 = adit = 0)[1 - m{t)/Q{t)]. (15) 

From (10) through (15) for the growth rate of a planet's radius we have 
(with J/ ^ 2): 

dr ^ {l + 2e)<ToWk 
dt 2tS 



r 26(2 + vy{t)iR/R„y i 

1 Za,R^[l + ey+''-{l-ey+-]j- ^ "'' 

It follows from (16) that the largest body which is not absorbed by the other 
bodies (a planet) ceases growing when it reaches a certain maximum radius 
(mass). The value of this radius is only determined by the parameters of 
the preplanetary disk. If we put a zero value in the bracket in (16), in the 
first approximation for e, we can yield max r, max m, max e, and max AR. 
In particular, 

max r = (^■^^j ■ s/2ad{R,0y'\ cm; 

The growth time scale is an integration (16). It is close to the one generated 
by Safronov (1969) and Wetherill (1980) and is on the order of 65-90 million 
years for accreting 80-90% of the mass. 

One can state the following for distances between two accreting planets: 

R„^i - Rr, faA„R + A„+iR = e„R„+e„+iR„+i, (18) 


Rr,+i/R^~{l + e„)/il-e„+i) = b. (19) 

In view of (17) the following theoretical estimate can be made for terrestrial 
planets: b(max e = 0.2-0.25) — 1.5-1.67. For the zone of outer planets 
b(max e = Gcr = 0.32-0.35) = 1.85-2.3. The real values b in the present 
solar system are cited in Tkble 1. The theory that was developed not only 
explains the physical meaning of the Titius-Bode law, but also provides 
a satisfactory estimate of parameter b. The partial overlapping of zones, 


TABLE 1 The real vilue* b in the prejent soUriyitan 

Venus- Earth- Mars- Asteroids Jupiter- Saturn- Uranus- Neptune- 


Mercury Venus Earth Mars Ceres Jupiter Saturn Uranus 

b 1.87 1.38 1.52 1.77 1.88 1.83 2.01 1.57 

embryo drift, and the effects of radial redistribution of matter (Vilyazev et 
al. 1990) complicates the formulae, but this does not greatly influence the 
numerical values max m, max e, and b. 

An estimate of the number of forming planets can easily be generated 
from (19) for a preplanetary disk with moderate mass and distribution cr(R) 
according to the standard or MK-models with pre-assigned outer and inner 

N = ^"(^*/^-) (20) 

ln[(l -I- max e)/(l - max e)] 

With low values of max e from (20) we have N ~ ln(R*/R.)/2 max e 
and yield a natural explanation of the results of the numerical experiment 
(Isaacman and Sagan 1977): N oc 1/e. For a circumsolar disk with initial 
mass ;S O.IM©, the theory offers a satisfactory estimate of the number of 
planets which formed: 

Niir < 10^ AU, R, > 10-^ AU, max e ~ e^ = 1/3) < 10. 


Workers were long unsuccessful in developing estimates of planet 
eccentricities, orbital inclinations, and mean periods of axis rotation, which 
were formed during the planets' growth process. In other words, estimates 
that fit well with observational data. Perchernikova and Vityazev (1980, 
1981) demonstrated that by taking into account the input of large bodies, 
the existing discrepancy between theory and observations could be resolved. 
When accreting planets approach and collide with large bodies at the 
earliest stages e increases. A rounding off of orbit takes place at the final 
stage: by the time accumulation is completed estimated values for e are 
close to present "mean" values (Laska 1988). The same can be said for 
orbital incUnations. Vityazev and Pechernikova (1981) and Vityazev et aL 
(1990) developed a theory for determining mean axial spin periods and axis 


inclinations. The angular momentum vector for the axial spin of a planet 
K, inclined at an angle e to axis z (z is perpendicular to the orbital plane), 
is equal to the sum of the regular component Ki, which is directed along 
axis z and the random component K2, which is inclined at an angle 7 to 
z. For Ki in a modified Giuli-Harris approximation (for terrestrial planets) 
the following was generated: 

1/4 , o \ 5/12 

^ 48 /20G/2MqV/V 3 Y 

my^Fiim/Q), F,{m/Q = 1) = 9.6 ■ 10"^ (21) 

Dispersion K2 is (q = 11/6): 

DK2 « 4.18 • 10- V'^Gm»°/3 . F^^rn/Q), Fiim/Q = 1) = 0.123. (22) 

The authors demonstrated that as planets accumulate what takes place is 
essentially direct rotation (c < 7 < 90°). Large axis rotation inclinations 
and reverse rotation of individual planets are a natural outcome of the 
accumulation of bodies of comparable size. It is clear from (21) and (22) 
that the theoretical dependence of the specific axis rotation mementum 
(oc m^/^) approaches what has been observed. It is worth recalling that 
this theory does not allow us to determine the direction and velocity at 
which a planet, forming at a given distance, will rotate. It only gives us the 
corresponding probability (Figure 4). 


Vityazev and Pechernikova (1985) and Vityazev et al. (1989) have 
repeatedly discussed the problem of fusing physico-mechanical and physico- 
chemical approaches in planetary cosmogony. We will only mention two 
important findings here. Vityazev and Pechernikova (1985, 1987) proposed 
a method for estimating the time scale for gas removal from the terrestrial 
planet zone. They compared the theory of accumulation and data on 
ancient irradiation by solar cosmic rays of the olivine grains and chondrules 
of meteorite matter with an absolute age of 4.5 to 4.6 billion years. 


It is easy to demonstrate that if gas with a density of at least 10~^ 
of the original amount remains during the formation of meteorite parent 
bodies in the preplanetary disk between the asteroid belt and the Sun, then 



•^1 - ^cz 
, ,'^°2cm2/c 


Ki + Kjj2 


, , 2 ■ io^^2cm2/c 


Ki +K 

^1 - K(jz 
, (^ .-, 0^*^2 0012/0 


Ki + Kcy2 

I 11-10 



2 crrr^/c 

FIGURE 4 Diagrams of the componenU of the momentum of planelaiy axis rotation. 
Vector K of the observed rotation is shown. An initial rotational period of 10 hours was 
assumed for Earth. A rotational period equal to 15 houre was assumed for Uranus. The 
lined area corresponds to reverse rotation. 


solar cosmic rays (high-energy nuclei of iron and other elements) could not 
have irradiated meteorite matter grains. Vityazev and Pechernikova (1985, 
1987) showed that irradiation occurred when 100- to 1000-kilometer bodies 
appeared. The reasoning was that prior to that time nontransparency of 
the swarm of bodies was still sufficiently high, while less matter would have 
been irradiated at a later stage than the 5-10% that has been discovered 
experimentally. The conclusion then follows that there was virtually no 
gas as early as the primary stage of terrestrial planet accumulation. This 
conclusion is important for Earth science and comparative planetology 
because it is evidence in favor of the view of gas-free accumulation of the 
terrestrial planets at the later stages and repudiates the hypothesis of an 
accretion-induced atmosphere (see, for example the works of the Hayashi 


According to current thinking, the Earth (and other planets) was 
formed from bodies of differing mass and composition. It is supposed that 
the composition of these bodies is, at least partially, similar to meteorites. 
Several constraints on the possible model composition of primordial Earth 
(generated by the conventional mixing procedure) can be obtained from a 
comparison of data on the location of meteorite groups and mafic bedrock 
on Earth on the diagram cr'^0 - <t'*0 and density data. Pechernikova and 
Vityazev (1989) found constraints from above on Earth's initial composi- 
tion with various combinations of different meteorite groups: the portion 
of carbonaceous chondrite-type matter for Earth was < 10%, chondrite 
(H, L, LL, EH, EL) < 70% and achondrite (Euc) -|- iron < 80%. They 
proposed a method which can be used to determine multicomponent mix- 
tures of Earth's model composition. The composition of Mars can also 
be determined from the hypothesis of the Martian origin of shergottites. 
Confirmation of the authors' hypothesis on the removal of the silicate shell 
from proto-Mercury (Vityazev and Pechernikova 1985; Pechernikova and 
\^tyazev 1987) would mean that there is an approximately homogeneous 
composition for primary rock-forming elements in the entire zone 0.5-1.5 


Vityazev (1982) and Safronov and Vityazev (1983) showed that by the 
stage where 1000-kilometer bodies are formed, there commences a moder- 
ate, and subsequently, increasingly intensive process of impact processing, 
heating metamorphism, melting, and degassing of the matter of colliding 
bodies. It has been concluded that > 90% of the matter of bodies which 




FIGURE 5 Estimates of the Earth's initial temperature: 1 is healing by small bodies 
(Safronov 1959); 2 is heating by large bodies (Safronov 1969); 3 is heating by large bodies 
(Safronov 1982); and 4 is heating by large bodies (Kaula 1980). The arrow indicates 
modifications in the estimates of T/Tn, since the 1950s, including the authors' latest 

went into forming the terrestrial planets had already passed the swarm 
through repeated metamorphism and melting, both at the surface and in 
the cores of bodies analogous to parent bodies of meteorites. 


If we take into account the collisions of accreting planets with 1000- 
kilometcr bodies, we conclude that there were extremely heated interiors, 
beginning with protoplanctary masses > IQ-^Me- The ratio of the earliest 
and current estimates for primordial Earth are given in Figure 5. The latest 
temperature estimates indicate the possibility that differentiation began in 
the planet cores long before they attained their current dimensions. 

The primary energy sources in the planets are known to us. In addition 
to energy released during the impact processes of accumulation, the most 
significant sources for Earth are: energy from gravitational differentiation 
released during stratification into the core and mantle ( ~1.5 103^ergs) and 
energy from radioactive decay ( < l-lO^^ergs). It is important for specific 
zones to account for the energy of rotation released during tidal evolution 
of the Earth-Moon system (~ lO^^'ergs) and the energy of chemical trans- 
formations < lO^^'ergs). However, these factors arc not usually taken into 


account in global models. The energy from radioactive decay at the initial 
stages plays a subordinate role. However, the power of this source may 
locally exceed by several times the mean value er(U,Th,K) ~ 10~^erg/cm^s 
(in the case of early differentiation and concentration of U, Th, and K 
in near-surface shelb). The power of the shock mechanism is significantly 
greater even on the average: eimp ~ 10"''-10~^erg/cm^s. Intermediate 
values are generated for the energy of gravitational differentiation cgd ~ 
10~'-10"®erg/cm^s (the time scale for core formation is 0.1 to one billion 
years) and the source of equivalent adiabatic heating during collapse of ~ 


Heat-mass transfer calculations in planetary evolution models are cur- 
rently made using variotis procedures to parameterize the entire system 
of viscous liquid hydrodynamic equations for a binary or even single- 
component medium. This issue was explored (Safronov and Vityazev 1986; 
Vityazev et al. 1990) in relation to primordial Earth. We will merely note 
here the order of values for effective temperature conductivities, which 
were used for thermal computations in spherically symmetrical models with 
a heat conductivity equations such as: 

f = l/H^^(i?^Ei.,|I) + Ee./,.,. (23) 

The value which is normally assumed for aggregate temperature conduc- 
tivity is a function of molecular mechanisms K^ = 10"^cm^/s. For shock 
mbting during crater formation, the effective mean is YUmp ~ 1-10 cm^/s. 
Similar values have effective values for thermal convection (K<; ~ 10"* -10 
cm^/s) and gravitational differentiation (Kgd ~ 1-10 cmj/s). It is clear from 
these estimates that the energy processes in primordial Earth exceeded by 
two orders and more contemporary values in terms of intensity. 


The planets were formed from bodies with slightly differing compo- 
sitions, and which accumulated at various distances. Variations in their 
composition and density were, on the average, on the same order as the 
adjacent planets: 

\Sc„\/cK\8po\l-p<Q.\ (24) 

These fluctuations were smoothed out during shock mixing with crater 
formation, but remained on the order of 



\Spo\ c^ \Sc\ = \6co\ li =i 10-^ - 10-^ (25) 

where ^(~10^- 10^) is the ratio of mass removed from the crater to the 
mass of the fallen body. Using the distribution of bodies by mass (6), 
we can estimate the distribution of composition and density fluctuations 
both for a value {8p) and for linear scales (1). For a fixed 6p, spaces 
occupied by small-scale and large-scale fluctuations are comparable. It can 
be demonstrated that during planet growth, relaxation of inhomogeneities 
already begins (floating of light objects and sinking of heavy ones). In the 
order of magnitude, velocity v, relaxation time scale r, effective temperature 
conductivity K and energy release rates e for one scale inhomogeneities 
occupying a part of the volume c, are obtained from the expressions: 

\v\ = \Sp\gllbn,T~Rllv\ (26) 

K oncvl, € ~ \bp\gc\v\\IR^, 

where g is the acceleration of gravity, and t} is the viscosity coefficient. 
Where g ~ lO^cm/s^, i^ ~ lO^" poise, Sp/p ~ 10-^ - 10-^ c ~ 0.1, 
we have M I 10"^ - 10-«cm/s, K 1 - lO^cm^/s, r ~ (1-10)106 
years, e < Cr(U,Th,K). Estimates show that, owing to intensive heat transfer 
during relaxation of such inhomogeneities, the accreting planet establishes 
a positive temperature gradient (central areas are hotter than the external). 
This runs contrary to previous assessments (Safronov, 1959, 1969, 1982; 
Kaula 1980). The second important conclusion is that heavy component 
enrichment may occur towards the center, which is sufficient for closing off 
large-scale thermal convection. This is due to relaxation of the composition 
fluctuations during planet growth. Both of these conclusions require further 
verification in more detailed computations. 


Peak heat releases, as these relatively large bodies fall, exceed by many 
orders the values for Ump which are listed above. Entombed melt sites seek 
to cool, giving off heat to the enclosing medium. However, density-based 
differentiation, triggering a separation of the heavy (Fe-rich) component 
from silicates, may deliver enough energy for the melt area to expand. 
Foregoing the details (Vityazev et al. 1990), let us determine the critical 
dimensions of such an area. Let us write (23) in nondimensional form: 

^ = A(l + Pe<,e«/")^0 -^ r • e« -f r., (27) 



RTl ' AXRTl ' '~ 4XRTI' " 


is the difference between heavy and light component densities, c is the 
heavy component portion in terms of volume, h is the characteristic size 
of the area (layer here), E is the energy for activation in the expression 
for the viscosity coefficient, A is the heat conductivity coefficient, Vo(9 = 
0) is the Stokes' velocity, or filtration rate, whose numerical value is found 
from the condition e,. == cov It can be demonstrated that for r > r^r 
(Fe = 0.88 for the layer and T^ = 3.22 for the sphere) and e > ©er 
(0er - 1.2 for the layer and Qcr = 1-6 for the sphere) with 9 = at 
the area boundaries, conditions are maintained which promote a "thermal 
explosion." The emerging differentiation process can release enough energy 
to develop the process in space and accelerate it in time. For Ap = 4.5 
g/cm^, pc = 0.2,pcp = 10«erg/cm3 K, RT^/E = 50K, as= IQ-^cm^/s, and a 
Peclet number < 1, critical dimensions of the area (her) are on the order 
of several hundred kilometers. 


Experimental data on meteorite material melt is too meager to make 
reliable judgements as to the composition of phases which are seeking to 
divide in the field of gravitational pull. Classical views, hypothesizing that 
the heavy (Fe-rich) component separates from silicates and sinks, via the 
filtration mechanism or as a large diapiere structures in the convecting shell, 
have only recently been expressed as hydrodynamic models. Complications 
with an estimate of the characteristic time scales for separation are, first 
of all, related to highly ambiguous data on numerical viscosity values for 
matter in the interiors. Variations in the temperature and content of fluids 
on the order of several percent, close to liquidus-solidus curves, alter 
viscosity numerical values by orders of magnitude. It is clear from this that 
even for Stokes' (slowed) flows, velocity v oc n~* and characteristic time 
scales r oc n are uncertain. Secondly, existing laboratory data point to the 
coexistence of several phases (components) with sharply varied rheology. 
This further complicates the separation picture. Nevertheless, a certain 
overall mechanism which is weakly dependent on concrete viscosity values 
and density differences, was clearly functioning with interiors differentiation. 
A number of indirect signs are evidence of this; they indicate the very early 
and concurrent differentiation of all terrestrial planets, including the Moon. 

The following are time scale estimates of the formation of the Earth's 


1) From paleomagnetic data, the core existed 2.8 to 3.5 billion years 


2) Based on uranium-lead data, it was formed in the first 100 to 300 

million years. 

(The following do not clash with items 1 and 2 listed above). 

3) Data on the formation of a protective, ionosphere or magne- 
tosphere screen for ^^Ne and ^^Ar prior to the first 700 million years, 


4) Data on intensive degassing in the first 100 million years for I-Xe. 


The solution (generated in the 1970's-80's at least in principle) to the 
primary problems of classical planetary cosmogony has made it possible to 
move towards a synthesis of the dynamic and cosmochemical approaches. 
The initial findings appear to be promising. However, they require con- 
firmation. Clearly, there is no longer any doubt that intensive processes 
which promoted the formation of their initial shells occurred at the later 
stages of planet formation. At the same time, if we are to make significant 
progress in this area, we will need to conduct experimental studies on 
localized matter separation and labor-intensive numerical modeling to sim- 
ulate large-scale processes of fractioning and differentiation of the matter 
of planetary cores. 


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Giant Planets and their Satellites: 

What are the Relationships Between Their Properties 

and How They Formed? 

David J. Stevenson 
California Institute of Tfechnology 


The giant planet region in our solar system appears to be bounded 
inside by the limit of water condensation, suggesting that the most abundant 
astrophysical condensate plays an important role in giant planet formation. 
Indeed, Jupiter and Saturn exhibit evidence for rock and/or ice cores or 
central concentrations that probably accumulated first, acting as nuclei for 
subsequent gas accumulation. This is a "planetary" accumulation process, 
distinct from the steUar formation process, even though most of Jupiter 
has a similar composition to the primordial Sun. Uranus and Neptune 
are more complicated and imperfectly understood, but appear to exhibit 
evidence of an important role for giant impacts in their structure and 
evolution. Despite some interesting systematics among the four major 
planets and their satelUtes, no simple picture emerges for the temperature 
structure of the solar nebula from observations alone. However, it seems 
likely that Jupiter is the key to our planetary system and a similar planet 
could be expected for other systems. It is further argued that we should 
expect a gradual transition from solar nebula dominance to intersteUar 
dominance in the gas phase chemistry of the source material in the outer 
solar system because of the inefficiency of diffusion in the solar nebula. 
There may be evidence for this in comets. Similar effects to this may 
have occurred in the disks that formed around Jupiter and Saturn during 
their accretions; this may show up in sateUite systematics. However, each 
satelUte system is distinctive, preventing general conclusions. 




In our solar system, over 99.5% of the known planetary mass resides in 
the planets beyond the asteroid belt, primarily in Jupiter, Saturn, Uranus, 
and Neptune. However, from the point of view of an earthbound cosmo- 
chemist, these bodies are not a "well known" (i.e. sampled) part of the solar 
system, but from the point of view of the astronomer seeking a general 
understanding of planetary system detectability and taxonomy, the giant 
planets should be the most important source of information. 

It is convenient to divide the constituents of planets into three compo- 
nents: 1) "gas" (primarily hydrogen and helium; not condensable as liquid 
or solid under solar system conditions); 2) "ices" (volatile but condensable 
to varying degrees; H2O is the most common, CO, CH4, NH3, and N2 are 
the other main ones); and 3) "rock" (essentially everything else; primarily 
silicates and metallic or oxidized iron). 

Jupiter defines a remarkable transition in our planetary system. Inside 
of Jupiter's orbit at 5 AU, the planets are small and rocky, largely devoid 
of both "ices" (especially water, the most abundant condensate in the 
universe) and "gas." By contrast, Jupiter has about 300 Earth masses of 
gas, and the more distant giant planets, though less well endowed, also have 
large reservoirs of gas. It is perhaps even more significant that Jupiter is the 
first place outward from the Sun at which water ice appears to become a 
common condensate. Although we do not know the abundance of water in 
Jupiter (because it forms clouds deep in the atmosphere), we see satellites 
such as Ganymede and Callisto which contain about as much ice as rock 
by mass, and we observe enhancements of other "ices" (CH4 and NH3) in 
the Jovian atmosphere. 

The outer edge of the solar system is ill defined. It is possible that 
the cometaiy cloud contains a greater amount of ice and rock than do 
all the giant planets combined, especially if the most massive comets are 
substantially larger than the comets we have seen. A more conservative 
estimate of total cometaiy mass is approximately 10 Earth masses, but some 
increase in this estimate is justified given the recent realization that Halley 
is more massive than previously suspected (Sagdeev et al. 1988; Marochnik 
et al. 1988). The inner part of the cometaiy distribution, sometimes called 
the Kuiper belt, has now been tentatively identified as a disk rather than a 
spherical cloud (Duncan et al. 1988) and is therefore clearly associated with 
the planetary formation process. Planet X (a body beyond Pluto) has been 
frequently mentioned as a possibility, but no firm corroborative evidence 
currently exists. 

One game that can be played is called reconstituting the nebula. One 
surveys the estimated amounts of rock and ice in each of the giant planets, 
then attempts to determine how much material of cosmic composition 


would be required to provide that much rock and ice. Roughly speaking, 
this implies that each of the four major planets required ~ 0.01 M© of 
cosmic composition material. The cometary reservoir may have required 
an amount comparable to each of the planets. The similarity for each 
giant planet arises because they have roughly similar amounts of ice and 
rock (10-20 Earth masses) but diminishing amounts of gas as one proceeds 
outwards. The planets are also spaced in orbits that define a roughly 
geometric progression. In other words, 

O.OIMq ~ / <T{R')2nR'dR', (1) 


independent of R, where a{R) is the "surface density" (mass per unit area) 
of the discoid nebula from which the planets form, and R is the (cylindrical) 
radius. This impUes (t(R) ~ (2 x IC g cm-^)fR^ where /? is in astronomical 
units. Theoretical models for a(R) from accretion disk theory tend to give 
somewhat weaker dependences on R, implying a stronger tendency for most 
of the mass to be near the outer limits of the nebula. Naturally, most of the 
angular momentum is also concentrated in the outer extremities. The outer 
radius of the solar nebula is not known, but was presumably determined 
by the angular momentum budget of the cloud from which the Sun and 
planets formed. 


One could say a lot about how giant planets formed if one knew 
their internal structures. However, there are as of yet no techniques that 
are similar to terrestrial or solar seismology and that enable inversion 
for the interior densities in a detailed way. Instead, one must rely on a 
very small set of data, the lower-order (hydrostatic) gravitational moments, 
and the correspondingly small number of confident statements regarding 
the interiors. Even if the quantity of information thus obtained is low, 
the quality is high and represents a quite large investment of theoretical 
and computational effort, together with some important experimental data 
from high-pressure physics. Although the theory is not ahvays simple, its 
reliability is believed to be high. The great danger exists, however, in 
overinterpreting the very limited data. 

Good reviews on the structure of giant planets include Zharkov and 
Tl-ubitsyn (1978), Stevenson (1982), and Hubbard (1984), and it is unnec- 
essary to repeat here the techniques, data, and procedures used. In the 
case of Jupiter, there is no doubt that ~ 90-95% of the total mass can 
be approximated as "cosmic" composition (meaning primordial solar com- 
position). However, the gravitational moment J2 (which can be thought 
of as a measure of the moment of inertia) indicates that there must be 


some central concentration of more dense material (ice and rock). The 
uncertainties in hydrogen and helium equations of state are not sufficient 
to attribute this central density "excess" to an anomalously large compress- 
ibility of H-He mixtures or even to a helium core (since the latter can be 
limited in size by the observational constraints on depletion of helium in 
the outer regions of the planet). There is no way to tell what the "core" 
composition is; it could be all rock or all ice or any combination thereof. It 
does not even need to be a distinct core; it only needs to be a substantial 
enhancement of ice and/or rock in the innermost regions. The amount of 
such material might be as little as five Earth masses but is probably in 
the range of 10 - 30 Earth masses. The upper range of estimates is most 
reasonable if a substantial portion of this heavy material is mixed upward 
into the hydrogen and helium. One important point for the purposes of 
understanding origin is that Jupiter is enhanced in rock and ice by roughly a 
factor of 10 relative to cosmic composition. In other words, Jupiter formed 
from a cosmic reservoir containing 10~^ solar masses, even though its final 
mass is only 10~^ solar masses, a fact we had already noted in the previous 
section. The other important point about the dense material: it probably 
did not accumulate near the center by rainout of insoluble matter. This is 
in striking contrast to the Earth's core which formed because metallic iron 
was both more dense and insoluble in the mantle (silicates and oxides). 
The temperature in the center of Jupiter is veiy high (> 20,000 K) and 
the mole fraction of the ice or rock phases, were they mixed uniformly 
in hydrogen, would not exceed 10"^. Although solubility calculations are 
difficult (Stevenson 1985), there does not seem to be any likelihood that 
some component would be Insoluble at the level of 10"^ mole fraction 
at r~ 20,000 K, since this requires an excess Gibbs energy of mixing of 
order kT In 100 ~ 8 ey well in excess of any electronic estimate based 
on pseudopotential theory. It seems likely that Jupiter formed by first 
accumulating a dense core; the gas was added later. Subsequent convective 
"dredging" was insufficient to homogenize the planet (Stevenson 1985). 

Saturn is further removed from a simple cosmic composition than 
Jupiter, a fact that can be deduced from the density alone since a body 
with the same composition as Jupiter but the same mass as Saturn would 
have about the same radius as Jupiter (Stevenson 1982). Saturn has only 
83% of Jupiter's radius, implying a dense core that causes contraction of 
the overfying hydrogen-helium envelope. In fact, the ice and rock core of 
Saturn has a similar mass to that of Jupiter, but this is a larger fraction of 
the total mass in the case of Saturn. An additional complication in Saturn's 
evolution arises because of the limited solubility of helium in metallic 
hydrogen, predicted long ago but now verified by atmospheric abundance 
measurements. The presence of a helium-rich deep region is compatible 
with the gravity field (Gudkova et al. 1988) as well as being required by 


mass balance considerations. As with Jupiter, the ice and rock central 
concentration must be primordial and form the nucleus for subsequent 
accretion of gas. 

Despite recent accurate gravity field information (Ftench et al. 1988) 
based on ring occultations, models for Uranus are not yet so well char- 
acterized. The problem lies not with the general features of the density 
structure, which are agreed upon by all modelers (Podolak et al. 1988), 
but with the interpretation of this structure, since no particular component 
(gas, ice, or rock) has predominance. A mature of gas and rock can behave 
like ice, leading to a considerable ambiguity of interpretation. There is no 
doubt that the outermost ~ 20% in radius is mostly gas, and it is generally 
conceded that some rock is present within Uranus (though not much in 
a separate, central core). It is clear that the models require some mixing 
among the constituents: it is not possible to have a model consisting of 
a rock core with an ice shell and an overlying gas envelope as suggested 
around 1980. It is not even possible to have a model consisting of a rock 
core and a uniformly mixed envelope of ice and gas. The most likely model 
seems to involve a gradational mixing of constituents, with rock still pri- 
marily concentrated toward the center, and gas still primarily concentrated 
toward the outside. 

Accurate models of Neptune must await the flyby in August, 1989. 
Based on the existing, approximate information it seems likely that the 
main difference between Uranus and Neptune is the extent of mixing of 
the constituents. Uranus has a substantial degree of central concentration 
(low moment of inertia), despite the inference of mixing described above. 
Neptune has a higher moment of inertia, suggesting far greater homoge- 
nization. At the high temperatures (~ lO"* K) and pressures (0.1 Mbar and 
above) of this mixing, phase separation is unlikely to occur, so the degree 
of homogenization may reflect the formation process (degree of impact 
stirring) rather than the phase diagram. 


Many of the minor constituents in giant planets undergo condensation 
(cloud formation) deep in the atmosphere and their abundances are ac- 
cordingly not well known. The main exceptions are methane (which either 
does not condense or condenses in a region accessible to occultation and. 
IR studies) and deuterated hydrogen (HD). Some limited information on 
other species (especially NH3) exists from radio observations, but we focus 
here on carbon and deuterium. 

Carbon is enriched relative to cosmic by a factor of two (Jupiter), five 
(Saturn), and ~ 20 (Uranus). At least in the cases of Jupiter and Saturn, the 


enhancement cannot be due to local condensation of the expected carbon- 
bearing molecules present in the primordial solar nebula (CC3 or CH4) even 
allowing for clathrate formation. This interpretation follows from the fact 
that water ice did not condense closer to the Sun than about Jupiter's orbit, 
yet any solid incorporating CO or CH4 requires a much lower temperature 
than water to condense (Lewis 1972). The enhancement of carbon must 
arise either through ingestion of planetesimals containing involatile carbon 
or "comets" (planetesimals that formed further out and were scattered into 
Jupiter-crossing orbits). There is increasing awareness of involatile carbon 
as a major carbon reservoir in the interstellar medium and it has long been 
recognized as a significant component of primitive meteorites. Comets also 
possess a substantial involatile carbon reservoir (Kissel and Kreuger 1987), 
but much of the cometary carbon reservoir is in C-O bonded material (part 
but not all as carbon monoxide; Eberhardt et al. 1987). If we are to judge 
from known carbonaceous chondrites, then the amount of such material 
needed to create the observed Jovian or Saturnian carbon enrichment is 
very large, 20 to 30 Earth masses, especially when one considers that this 
must be assimilated material (not part of the unassimilated core). Comets 
would be a more "efficient" source of the needed carbon, but it is also 
possible that the currently known carbonaceous chondrites do not reflect 
the most carbon-rich (but ice-poor) material in the asteroid belt and beyond. 
Even with comets, one needs of order 10 Earth masses of material added to 
Jupiter after it has largely accumulated. The implication is that estimates 
of ice and rock in Jupiter or Saturn, based solely on the gravity field, are 
likely to be lower than the true value because much of the ice and rock is 
assimilated (and therefore has no clean gravitational signature). 

In Jupiter and Saturn, the value of D/H ~ 2 x 10~* is believed to 
be "cosmic." However, this interpretation is still imperfectly established 
because of uncertainties in the "cosmic" value, and its true meaning (i.e., is 
it a primordial, universal value?). A cosmic value seems like a reasonable 
expectation, but it must be recognized that there are very strong fraction- 
ation processes in the interstellar medium which deplete the gas phase 
and enrich the particulate material. This enrichment is well documented 
for meteorites and is also probably present in comets. It is likely that the 
gaseous component of pro to Jupiter was depleted in deuterium, but that the 
assimilation of the carbon-bearing solids described above also contributed 
deuterium-rich materials, probably more than compensating for the gas- 
phase depletion. Thus, D/H in Jupiter is probably in excess of cosmic, 
though perhaps not by a large enough factor to be detectable in the current 
data. In contrast, Uranus is clearly enriched (D/H ~ 10~^), an expected 
result given the far higher ratio of ice or rock to gas in that planet and 
the evidence of at least partial mixing discussed earlier. Neptune might be 


expected to have an even larger D/H if it is more substantially mixed than 

In summary, atmospheric observations provide additional evidence of 
noncosmic composition and partial assimilation of "heavy" material (ice 
and rock) into the envelopes of giant planets. 


Jupiter, Saturn, and Neptune emit more energy than they receive from 
the Sun, implying significant internal energy sources. The uhimate source of 
this energy is undoubtedly gravitational, but there are several ways in which 
this energy can become available. In Jupiter, the heat flow is consistent 
with a simple cooling model in which the planet was initially much hotter 
and has gradually cooled throughout the age of the solar system. In this 
case, the gravitational energy of accretion created the primordial heat 
reservoir responsible for the current heat leakage. In Saturn, the heat 
flow is marginally consistent with the same interpretation, but the observed 
depletion of helium in the atmosphere requires a large gravitational energy 
release from the downward migration of helium droplets. This process may 
also contribute part of the Jovian heat flow. Even with heUum rainout, it 
is necessary to begin the evolution with a hot planet (at least twice as hot 
as the present interior thermal state), but this constraint is easily satisfled 
by accretion models. 

Uranus and Neptune have strikingly different heat flows. The Uranus 
internal heat output is less than 6 x 10^' erg/s and might be zero; expressed 
as energy output per gram, this is an even lower luminosity than the Earth. 
The Neptune heat flow is about 2 x 10^^ erg/s. Although clearly much 
larger, it is still less than one would expect if Neptune were fully adiabatic 
and began its evolution with an internal temperature of at least twice 
its present value (the assumption that works so weU for Jupiter). The 
difference between Uranus and Neptune is striking and not easily explained 
solely by their different distances from the Sun. It is also unlikely that these 
planets began "cold," that is, only slightly hotter than their present states 
since the energy of accretion is enough to heat the interior by ~ 2 x ICK. 
The low heat flow of Uranus may be due to stored heat of accretion; this 
heat is unable to escape because of compositional gradients, which inhibit 
thermal convection. In this way one can reconcile the low heat flow of 
Uranus with a high heat content and the inferred partial mixing of the 
interior discussed above (Podolak et al. 1990). By contrast, Neptune has a 
relatively high heat flow because it is more uniformly mixed. A speculative 
explanation for this difference in mixing efficiency is that the last giant 
impact on Uranus was oblique and created the large obliquity and disk 
from which the sateUites formed. This impact was not efficient in mixing 


the deep interior. By contrast, the last giant impact on Neptune was nearly 
head on, which is a more efficient way of heating and mixing the interior 
and did not lead to the formation of a compact, regular satellite system. 
The high heat flow of Neptune is accordingly related to its higher moment 
of inertia. This speculation may be testable after the Voyager encounter at 

In summary, the heat flows of giant planets support the expectation 
that these planets began their life hot. In some cases (e.g., Jupiter) much 
of this heat has since leaked out. In at least one case (Uranus) the heat 
has been stored and prevented from escaping by compositional gradients 
which inhibit convection. 


The four giant planets exhibit a startling diversity of satellite systems. 
Jupiter has four large, comparable mass satellites with a systematic variation 
of density with distance, suggesting a "miniature solar system." Saturn has 
an extensive satellite system, though only one of the satellites (Titan) is 
comparable to a Galilean satellite. Uranus has a compact family of icy 
satellites, regularly spaced and in the equatorial plane. Neptune has only 
two known satellites, in irregular orbits. One of these is THton, a large 
body that has significant reservoirs of CH4 and possibly N2. Satellites 
are common, and they probably have diverse origins (Stevenson et al. 
1986). Some of the diversity may arise as the stochastic outcome of a 
common physical process (this may explain the difference between Jovian 
and Saturnian systems) but the Neptunian system is clearly different. One 
suspects that the Uranian system has a different history also, since it formed 
around a planet that was tipped over and never had as much gas accretion 
as Jupiter or Saturn. The recent enthusiasm for an impact origin of the 
Earth's Moon suggests that the Uranian system deserves similar attention. 
Impact origin seems to make less sense for Jupiter and Saturn, where the 
target is mostly gas, even though these planets must also have had giant 
impacts. The issue for Neptune is unresolved, though one wonders how a 
distant, nonequatorial, and inwardly evolving satellite such as IViton could 
have an impact origin. Perhaps Triton was captured. 

The formation of Jovian and Saturnian satellites is commonly at- 
tributed to a disk associated with the planet's formation, and therefore 
crudely analogous to solar system formation. Pollack and Bodenheimer 
(1988) discuss in some detail the implications of this picture. Even if a 
disk origin is accepted, there are two distinct circumstances from which 
this disk arises. One scenario involves the formation of satellites from the 
material shed by a shrinking protoplanet. In this picture, protoJupiter once 
filled its Roche lobe, then shed mass and angular momentum as it cooled. 


An alternative view is an accretion disk which forms and evolves before 
Jupiter or Saturn approaches its final mass. In this picture, the disk serves 
a role more similar to that of the solar nebula, though with some important 
dynamical differences: it is more compact (because of tidal truncation), 
and it is evolving more rapidly relative to the accretion time (whereas the 
viscous evolution time and accretion time are roughly comparable in the 
solar nebula). The solar system analogy must be used with care when 
applied to satellite systems! The choice between a disk that is shed and a 
true accretion disk has important implications for the chemistry (Stevenson 
1990) but must be resolved by future dynamical modeling. 


Is there evidence in the outer solar system for the expected temperature 
gradient of the solar nebula? Perhaps surprisingly, the answer is no. There 
is a trend of decreasing gas content in giant planets as one goes outward, 
but this surely reflects formation time scales and the ability of a proto- 
giant planet to accrete large amounts of gas before the onset of T Tiuri. 
Satellite compositions seem to reflect more the immediate environment of 
the central planet than the background temperature of the nebula. The lack 
of CO in Titan, and presumably TCton, may reflect the processing of solar 
nebula CO into CH4 in the disk or envelope surrounding the proto-giant 
planet, rather than any statement about solar nebula conditions. The only 
statement about temperature that seems reasonably firm is the placement of 
water condensation (T ~ 160 K) at around 5 AU at the time of condensate 

Of course, absence of evidence is not the same as evidence of absence. 
Nevertheless, we have to admit that we know remarkably little about the 
temperature variation in the solar nebula, either spatially or with time. 
One possible constraint could arise if there were a better knowledge and 
understanding of chemical trends in the outer solar system. For example, 
chemical processing such as catalyzed hydrogenation of CO to CH4 and 
higher hydrocarbons is thermally mediated. The contamination by the 
products at greater radii in the nebula depends on where these reactions are 
quenched and how quickly or efficiently the species are dispersed by winds 
and turbulent diffusion. Stevenson (1990) has argued that the transport is 
inefficient so that the more distant regions of the nebula are dominated 
by interstellar speciation. Prinn (1990) has pointed out, however, that the 
uncertainties in momentum and species transport make it difficult to reach 
firm conclusions. In any event, chemical indicators are the best hope for 
obtaining information on outer solar system temperatures. If comets are 
found to have compositional trends as a function of formation position (as 
is suspected for asteroids) then these may provide the best clues. 



The formation of the giant planets remains a major theoretical prob- 
lem. Evidence presented above supports the idea that these planets may 
have formed by accumulating a core of ice and rock first, with gas accretion 
following — but truncated at some point, presumably because of the T Tliuri 
mass loss or perhaps (in Jupiter's case) by tidal truncation of the accretion 
zone (Lin and Papaloizou 1979). The problem lies in the accumulation of 
the rock-ice core on a sufficiently short time scale, so that the gas is still 
present. Conventional accumulation models, based on Safronov's theory 
(1969) predict long time scales (> 10^ years), even with allowances for gas- 
drag effects (Hayashi et al. 1985). Rock-ice cores may begin to accumulate 
gas when they are only approximately one Earth mass (Stevenson 1984) 
and this aids the accumulation somewhat, but does not solve the problem. 
Lissauer (1987) pointed out that if the surface density of solids is sufficiently 
high in the region of Jupiter formation then a runaway accretion may take 
place, forming the necessary Jupiter core in ~ 10^ years. The onset of ice 
condensation helps increase the surface density by a factor of three, but 
this may not be sufficient by itself. Stevenson and Lunine (1988) suggest 
that a further enhancement may arise because of a diffusive transport of 
water molecules from the terrestrial zone into the Jupiter formation region. 
Several criteria must be satisfied to make this work well and they may not 
all be met. However, even a modest additional enhancement of the surface 
density in this region may make the mechanism work, at least to the extent 
of favoring the first (largest) giant planet at the water condensation front. 

This suggests a speculative prediction for other planetary systems: 
giant planets should occupy the region outward from the point of water 
condensation. The largest of these (the extrasolar equivalent of Jupiter) 
may be near the condensation point. This position will vary with the 
mass of the central star (or with the mass of the nebula that the star 
once had) but is presumably a calculable quantity as a function of star 
mass and angular momentum budget. We await the exciting prospect of 
identifying Jupiters and superJupiters about nearby stars and characterizing 
their orbital distributions and properties. 

The 1989 flyby of Neptune by Voyager reveals that Uranus and Nep- 
tune are more similar in structure than suggested above. This reduces 
the strength of argurneiits presented here for the role of giant impacts. 
TYemaine (preprint 1990) has suggested that the obliquity of Uranus is not 
related to impact 


This work is supported by NASA Planetary Geology and Geophysics 


grant NAGW-185. Contribution number 4686 from the Division of Geolog- 
ical and Planetary Sciences, California Institute of Tfechnology, Pasadena, 
California 91125. 


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Woweries, U. Stubbemann, RR. Hodges, J.H. Hoffman, and J.M. Illiano, 1987. 

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N91-22973 J 

The Thermal Conditions of Venus 

Vladimir N. Zharkov and V.S. Solomatov 
Schmidt Institute of the Physics of the Earth 


This paper examines models of Venus' thermal evolution. The models 
include the core which is capable of solidifying when the core's temperature 
drops below the liquidus curve, the mantle which is proposed as divided into 
two, independent of the convecting layers (upper and lower mantle), and the 
cold crust which maintains a temperature on the surface of the convective 
mantle close to 1200° C. The models are based on the approximation of 
parametrized convection, modified here to account for new investigations 
of convection in a medium with complex rheology. 

Venus' thermal evolution, examined from the point when gravitational 
differentiation of the planet was completed (4.6 billion years ago), is divided 
into three periods: (1) adaptation of the upper mantle to the thermal 
regime of the lower mantle: approximately 0.5 billion years; (2) entry of 
the entire mantle into the asymptotic regime approximately three to four 
billion years; (3) asymptotic regime. The parameters of a convective planet 
in an asymptotic regime are not dependent on the initial conditions (the 
planet "forgets" its initial state) and are found analytically. The thermal 
flux in the current epoch is ~50 ergs cm^s"'. We consider the connection 
between the thermal regime of Venus' core and its lack of magnetic field. 
After comparing the current thermal state of thermal models of Venus and 
Earth, together with the latest research on melting of the Fe-FeS system 
and the phase diagram of iron, we propose that Venus' lack of its own 
magnetic field is related to the fact that Venus' core does not solidify in the 
contemporary epoch. The particular situation of the iron triple point (7 - 
£ - melt) strengthens this conclusion. We discuss the thermal regime of the 





Venusian crust. We demonstrate that convection in the lower portion of 
the crust plays a minor role in regions with a particular crust composition, 
but that effusive or intrusive heat transport by melt, formed from melting 
of the crust's lower horizons, is the dominant mechanism for heat transport 
to the surface. 


Models of Venus' thermal evolution, calculated in approximation of 
parameterized convection (AFC), were examined in the works of Schubert 
(1979); Tbrcotte et al. (1979); Stevenson et al. (1983); Solomatov et al. 
(1986); and Solomatov et al. (1987). In parameterizing, dependencies were 
used that were obtained from studying convection in a liquid with constant 
viscosity. They were inferred to be true in cases of more complex rheol- 
ogy. New numerical investigations of convection in media with rheology 
that is more appropriate for the mantle (Christensen 1984a, b, 1985a, b) 
and theoretical research (Solomatov and Zharkov 1989) necessitated the 
construction of a modified APC (MAPC). 

Let the law of viscosity be expressed as (Zharkov 1983): 

,, = fc/r'"-'exp [Ao/T{plpof] (1) 

where r denotes the second invariant of the tensor of tangential stresses, 
p is density; b and L are considered here to be the constants within the 
upper and lower mantles; m « 3; A<, denotes the enthalpy of activation for 
self diffusion (in K); and where p = po is the reference value of density 
selected at the surface of each layer. 

Tb describe convection in such a medium, following Christensen (1985 
a), we will use two Raleigh figures: 

^ a^p^r^ 
j,ar = ^^^^^. (3) 


where a denotes the thermal expansion coefficient; g is the acceleration of 
gravity; AT is the mean superadiabatic temperature difference in the layer; 
d denotes layer thickness, x is the coefficient of thermal diffusivity; and %}„ 
and rfr are defined by the formulae: 

h Ao X , . 


The dependence of the Nusselt number (determined in terms of the 
thickness of the thermal boundary layer 6) on Ra,, and Ray, where m = 3, 
is parameterized by the formula 

Nu=-^=aRa^°Rap'. (6) 

In the case of free boundaries (lower mantle): 

a = 0.29, /3o = 0.37, ;?t = 0.16. (7) 

In the case of fixed boundaries (upper mantle): 

a = 0.13, ;3<, = 0.35, /?t = 0.15. (8) 

The theoretical expression has the following appearance (Solomatov 
and Zharkov 1989): 

Nu=n- ^"^ "*" ^ Raf^ Raf^' = 0.23/2a° ''Sa?,^. (9) 

^1 T7» ^p ^ I 

It is obtained from the balance of the capacities of viscous dissipation and 
buoyancy forces, and is in good agreement with (7) and (8). 

The heat flow at the upper or lower boundary of the layer is equal to 

F, = ^, (.0) 

where ATj denotes the temperature difference across the thermal boundaiy 
layer. Velocities at the boundary (u), mean tangential stresses in the layer 
(r) and mean viscosity (^) are estimated by the formulae (m=3): 

TTUb 1 ' - ^ 


-=[-r^^^{-r - (12) 

- \ If 

The mean temperature of the layer, T, and the temperature of the top of 
the lower thermal boundary layer, T^,, can be calculated from the adiabatic 
relationship through the temperature in the base of the upper thermal 
boundary layer, T„: 

T=nT„; ri=niT„, (14) 

where n and hl are constants. 


With large Rax/Rao, the very viscous upper thermal boundary layer 
becomes reduced in mobility, taking an increasingly less effective part in 
convection, and the previous formulae are not applicable. Solomatov and 
Zharkov (1989) estimated that the transition to a new convective regime 
occurs when 

Raj ^ Rartr « 2Ra^; m = 3. (15) 


There is no unequivocal answer to the question of whether convec- 
tion in the Earth's mantle (or Venus') is single layered or double-layered. 
Previous works explored the single-layered models of convection. Possi- 
ble differences in the single- and double-layered model of Venus' thermal 
evolution were discussed by Solomatov et al. (1986) and Solomatov et al. 
(1987). We propose here that convection is double-layered, and the bound- 
ary division coincides with the boundary of the second phase transition at 
a depth of approximately 756 kilometers (Zharkov 1983). 

The thermal model of Venus (Figure la) contains a cold crust, whose 
role is to maintain the temperature in its base at approximately 1200° C 
(melting temperature of basalts), the convective upper mantle, the con- 
vective lower mantle, and the core. An averaged, spherically symmetric 
distribution, T (r,t) is completely determined by the temperatures indicated 
in Figure lb. 

The thermal balance equations for the upper mantle, the lower mantle, 
and the core are written as: 

^ir(it!i - Rh)PiCpi^ = 4nRJ,F,2-^^RlFi„ (16) 

lw{R^y2-R^c)P2Cp2^ = l7r{R^n-t^c)P2Q2-inR]2F2i+^^RlFc, (17) 

-l^R'C,.Pc§ + Q^^= 4^«c^c. (18) 

Indices "1," "2," and "C relate, respectively, to the upper mantle, 
lower mantle and the core. T denotes the mean layer temperature, F^ is 
the heat flow from the mantle under the lithosphere. The heat flow at the 
surface of the planet is obtained by adding to Ft, thermal flow generated 
by the radiogenic production of heat in the crust (~11 erg cm~'s~^). The 
radius of the lithosphere boundary (R^) differs little from the radius of 
the planet (Ro) so that Ri, w Ro. It is supposed that almost all of the 
radioactive elements of the upper mantle migrated into the crust when the 



\ "^ 

T, = 1200'C 

T, = 460°C 

R„ S\ R„ R 

FIGURE 1 (a) Diagram of Venus's internal structure. Radii are indicated for: the 
planet — R,,; the base of the lilhosphere — R^; the boundary between the upper and 
lower mantles — R12; the core — Rd and the solid internal core — R,-. The dashed line 
illustrates the boundary of the lithosphere, which is an isothermlc surface of T5 = 
1200° C = const; dcr and di denote the thickness of the crust and the lithosphere. (b) 
Schematic, spherically symmetric temperature distribution in the cores of Venus. Reference 
temperatures aiie indicated for: the surface — T,; lithosphere base — Ts; base of the upper 
thermal boundary layer of the upper mantle— Tui; peak of the lower boundary layer of 
the upper mantle — T^i; boundary between the upper and lower mantles — T12; base of 
the upper boundary layer of the lower mantle — 7^2', peak of the lower boundary layer 
of the lower mantle — Tl2\ and ihe boundary between the core and the mantle — Tcm- 
Thicknesses of the thermal boundary layers are given: 5i for the boundaries of the upper 
mantle; 62 and 6c for the boundaries of the lower mantle. The dashed line indicates 
the core melting curve, which intersects the adiabatic temperature curve at the boundary 
between the outer, liquid and inner, solid core. 

crust was melted. Fc denotes the heat flow from the core. The heat flow 
at the boundary between the upper and lower mantles with a radius of R12 
is continuous: F12 = F2i- 

Heat production in the lower mantle (Q2) is defined by the sum 

Q2 = l]Qo.exp[A,0„-0] 



where Qoi and A, denote the current heat production of the radioactive 


isotopes K, U, and Th for one kilogram of undifferentiated silicate reservoir 
of the mantle and their decay constants. The concentrations of K, U, and 
Th are selected in accordance with O'Nions et al. (1979): U = 20 mg/t, 
KAJ = l(y, Th/U = 4. 

The term, Qc dm/dt, in (18) describes heat release occurring when 
the core solidifies after the core adiabat drops below the core liquidus 
curve. It is supposed that the core consists of the mixture, Fe-FeS, and 
as solidification begins from the center of the planet, sulfur remains in 
the liquid layer, reducing the solidification temperature. The value Qc is 
composed of the heat of the phase transition and gravitational energy. 

According to the estimates of Loper (1978); Stevenson et al. (1983), 
and Solomatov and Zharkov (1989), Q^ = (1-2) • lO^Oerg g-^. 

Mean temperature of the adiabatic core: 

T, « n,TcM (20) 

where n<: « 1.2, the mean core density is ^ = 10.5 g cm~^, Cpc = 4.7- 10^ 
erg g-' K-' (Zharkov and Ti-ubilsyn 1980; Zharkov 1983). 

The formulae for the melting T,„(p) and adiabatic Tad(p) curves are 
written as follows: 

/ \2.24 

T.(p) = T„(l-a.)(^J ' (21) 

T.4p) = Tcrr. (-^) , (22) 

\Pcm / 

-1.224 -0.009405-^- 0.1586 T-^j - 0.05672 T-^j . (23) 



Here T<, denotes the temperature at which pure iron melts at the boundary 
core of the radius Re, where p = pcu = 9.59 g cm"^; a « 2; x is the mass 
portion of sulfur in the liquid core, depending upon the radius of the solid 
core R, and the overall amount of sulfur in the core, x,,: 

The intersection of (21) and (22) defines the radius of the solidified core 
Rj (Figure lb). 

Convection in the upper mantle is parameterized by the MAPC with 
the parameters (7) (for fixed boundaries) in the lower mantle; and by the 
same formulae with the parameters (8) (for free boundaries). However, 
the difference between (7) and (8) is not very substantial. The parameters 
for the upper mantle are: bi = 4.3 • lO'^dyne^cm-^s, A^i - 6.9 • lO^K, 


oci = 3 ■ 10-^K-^ ^1 = 3.7 g cm-^, xi = IQ-^cm-^s-', ae, = 4.5 • lO'erg 
cm"*s- lO'^erg g 

and for the lower mantle: 

b2 = 1.1 • IQi'^dyne^cm-^s, A^z = 1.3 • 10% ocj = 1.5 • lO-^K-^, p^ 
= 4.9 g cm-3, X2 = 3 • lO-^cm-^s-S ae2 = 1.8 ■ lO^erg cm-^s-^K-S g = 
900cm s-2, Cp2 = 1.2 • lO^erg g-\ nz = 1.13, nL2 = 1-26. 



The evolution of the planet began approximately 4.6 billion years ago. 
The initial state of the planet was a variable parameter. The initial value 
of Tu2 is the most significant, since Tui, due to the low thermal inertia 
of the upper mantle, rapidly adapts to the thermal regime of the lower 
mantle (t < 0.5 billion years). The core has little effect on the evolution of 
the planet in general and the majority of models do not take into account 
its influence. T„2 was selected as equal to 2500, 3000, 3500 K The upper 
value is limited by the melting temperature of the mantle, since a melted 
mantle is rapidly freed from excess heat. 

The upper mantle adapts to the thermal regime of the lower mantle for 
the first approximately 0.5 billion years (Figure 2a, b). Then, after approx- 
imately three to four billion years the entire mantle enters an asymptotic 
regime which is not dependent upon the initial conditions. The evolution 
picture in general is similar to the one described by Solomatov et al. (1986); 
and Solomatov et al. (1987). The planet is close to an asymptotic state in 
the present epoch. Contemporary parameters of the models are: 

T„i = (1700-1720) K, ui = (2.1-2.4)cm yr-^ 

Ti2 = (2500-2530) K, U2 = (0.8-1.0)cm yr-^ 

T„2 = (2840-2870) K, ri = (5-6) bars, 

Fi = (35-40)erg cm-^ s"', 7=2 = (110-120) bars, 

0-1 = (28-30)km, ^1 = (1-2)10^1 poise, 

0-2 = (130-140)km, ^2 = (3-10)10^2 poise. 

According to the criterion (15) MAPC are applicable throughout the 
entire evolution, just as with the quasistationary criterion (Solomatov et al. 

The asymptotic expression for F^ in the first approximation is formu- 
lated as (Solomatov et al. 1987): 


Fl = Fg (^1 + -^ j , (25) 

where Fq denotes the thermal flow created by the radioactivity of the lower 
mantle, and tr is the characteristic time of decay: 











1 - T ,(0) = 2500K 

2 - t"2(0) = 3000K 

3 - \j(0) = 3500K 

2 3 








1 - T JO) = 2500K 

2 - T ,(0) = 3000K 

3 - T„j(0) = 3500K 

FIGURE 2 (a) Evolution of the base temperatures, Tui, Tj2 and Tu2i with differing 
initial conditions. The core is not taken into account and is considered to be Tcm — '^L2 
(Figure 1). (b) Evolution of the thermal flow under the lithosphere, Fjr,, with differing 
initial conditions. The thermal flow to the surface is obtained by adding ~ 11 erg cm~ s~ 
to F/,, generated by the radioactive elements of the crust. The dashed line indicates the 
thermal flow generated by radioactive elements of the lower mantle. 


equal ~5.67 • 10^ years at the current time. 

The time scale of thermal inertia of the mantle is equal to 

tin ^ Unl + ti„2il + S), (27) 

where ti„i and t,>,2 are the time scales for the inertia of each of the layers 


M2Q2 \ T^i ^J_. 

"2Cp2Ar2 f, , ^ , 02A2{T^2-Tn) \ 


ATi 1 + riLi? 1 + ^0 + /?2 - l/3(/?„ - 202)Ao2{Tu2 - T,2)T-^ ,^^. 
AT2 1 1 + /?i+/?i>Ii(T„i-Tb)T-i2 

Ml and M2 denote the layer masses, s = Ri2^ / Ri^. The values of (27) 
through (30) are calculated in a zero approximation: Fl = Fq, and A = 
Ao/n (p/pof. 

The time scale for thermal inertia, as compared with models based on 
the conventional APC (Solomatov et al. 1986, 1987), has increased from 
~ 2.5 • 10^ years to ~3.5 • 10^ years. The mantle and core temperatures 
obtained are somewhat lower (by 300 K near the core). In the models with 
the core, Tcm « 3720K and F^ « 15 erg cm~^s~^ in the contemporaiy 
epoch. Since the adiabatic value is Fc w 30 erg cm~^s~\ there is no con- 
vection if solidification is absent, and a magnetic field cannot be generated 
(Stevenson et al. 1983). 


We will estimate the temperatures in the Earth using the MAPC. 
MAPC is not applicable to the Earth's upper mantle, since convection in 
the Earth involves the surface layer, and rheology is, in general, more 
complex. However, MAPC is applicable to the Earth's lower mantle. Let 
us assume a value for the temperature at the boundary between Earth's 
upper and lower mantles of 

T12 = (2300 - 2500) /f, (31) 

(Zharkov 1983), and the thermal flow at this boundary is 


^(F-F. + C,M,^)« 

"31 ~ - - -- - --'' 

where F - Fcr » 70 erg cm"^s~^ is the medium thermal flow from the 
Earth, after deducting heat release in the crust (according to the estimates 
of Sclater et al. 1980), dTi/dt « -lOOK/billion years. (Basaltic Volcanism 
Study Project 1981). 

We will assume the following values for the rheologic parameters: 

6 = 6.6 • lO^Uyne^cm-^s, A = 1.5 • WK, andAo = 1.3 ■ 10" K. 

The remaining parameters are listed in Zharkov (1983). 
As a result, we have: 

Tu2 = (2800-2900) K, 
Ti,2 = (3600-3800) K, 
Tcm = (3800-4000) K, 
62 = 100 km. 

The value of T^^ - Ti,2 depends upon F^, which we will assume to be equal 
to the adiabatic value of Fad *« 30 erg cm~^s~^ 

Therefore, the temperature at the boundary of the Earth's core, Tcme 
is greater than for Venus (Tcmv) by a value of 

TcME - Tcmv = (100 - ZOO)K. (33) 

In order for Venus' core not to solidify, it is necessary that the adiabat of 
the Venusian core not drop below the solidification curve during cooling. 
Otherwise, solidification of the core will cause the core to mix by chemical 
or thermal convection, and it will trigger the generation of a magnetic field 
(Stevenson et al. 1983). We will estimate the difference between Tcme and 
the temperature, T^v (which is critical for the beginning of solidification), 
at the boundary of Venus' core, with a single pure iron melting curve, T^ 
(P) and a single equation of the state for iron p(?). 

Tcme is found from the intersection of the adiabat of the Earth's 
core (22) and the liquidus curve (23), with a sulfur content in the core 
of xe at the boundary of the Earth's inner core. Tcrv is obtained from 
the intersection of the adiabat of Venus' core (22) and the liquidus curve 
(23) with a sulfur content of x^. We then obtain (Solomatov and Zharkov 

Tcme - T„v = (+300) ^ (-300), K, (34) 


where x^- xv = ^ 0.07. Therefore, if xy ^ xg - (0 -^ 0.02) = 0.07 
-^ 0.12; (with x^ = 0.09 -^ 0.12; Aherns 1979), the core of Venus is not 
solidifying at the present time, and a magnetic field is not being generated. 

Complete solidification of the core would have led to the absence 
of a liquid layer in the core and would have made it impossible for the 
magnetic field to be generated. However, for this, the temperature near 
the boundary of Venus' core should have dropped below the eutectic value, 
which, according to the estimates of Anderson et al. (1987) is ~ 3000 
K and according to Usselman's estimate (1975) is ~ 2000 K. Such low 
temperatures of the core seem to be of little probability. 

Pressure in the iron triple point, 7 — e— 1, (liquid) approaches the 
pressure in the center of Venus. This is significant for interpretation the 
absence of the planet's own magnetic field. According to the estimates 
of Anderson (1986), P(p ss 2.8 Mbar (Figure 3), but is also impossible 
to rule out the larger values of Pjp. In the center of Venus, P<;„ rs 2.9 
Mbar; at the boundary of the solid inner Earth's core, P/b = 3.3.Mbar; 
and in the Earth's center, ?ce = 3.6 Mbar (Zharkov 1983). If ?„ ;S 
?tp, the conclusion that there is no solidification of Venus' core is further 
supported, since, in this case, the core's adiabat (critical for the beginning 
of solidification) drops several hundred degrees lower. This stems from the 
fact that reduction in the temperature of solidification of the mixture, 7- 
Fe - FeS is greater than for the mixture e- Fe - FeS by AS^/AS^ times, 
where ASe/AS.^ denotes the ratio of enthropy jumps (during melting) equal 
to ~ 2, according to Anderson's estimates (1986). 

The latest experimental data on the melting of iron allow us to estimate 
the melting temperature in the cores of Earth and Venus. Figure 3 shows 
melting curves obtained by various researchers, and the j - c boundary, 
computed by Anderson (1986). With x = 0.09-0.12 and o = 1 -r 2 (formula 
21), the full spread of temperatures at the boundary of the Earth's core, 
leading to the intersection of the liquidus and adiabat curves, is equal to 

TcA/E = 3500-=- 4700/1:, (35) 

- with data from Brown and McQueen (1986) and 

TcMB = 4300 ^ 5400K, (36) 

- with data from Williams et al. (1987). 

The effect of pressure on viscosity of the lower mantle reduces the 
effective Nusselt number and increases the temperature of Tcme and 
TcMv by ~ 300 K (Solomatov and Zharkov 1989). We obtain the estimate 

Tcme = 3800 H-4300A', (37) 

which is the best fit with (35). 







8000 r 











































I 2 

Pressure, Mbar 

FIGURE 3 Pure iron melling curves according to various data and the boundary of the 
phase transition 7 — Fc — t^Fe. Tlie figures indicate melting curves: 1 is from the study 
by Wilhams « al. (1987); 2 is from the study by Anderson (1986) and experimental data 
from Brown and McQueen (1986); and 3 is based on the Lindeman formula with the 
Grunehaisen parameter of G = 1.45 = const, using experimental data from Brown and 
McQueen (1986). Tlic transition boundary, 7— e, was constructed in the study by Anderson 
(1986) and together with the melting curve gives us the location of the triple point. The 
vertical segments illustrate errors in determining temperature for curves 1 and 2. The 
boundary labels arc as follows: CM is the boundary between the core and the mantle; C 
denotes the center of the planet; I is the boundary of the solid inner core; and the final 
letter indicates Earth (E) or Venus (V). 7 - f - I denotes the location of the triple point. 


What arc the mechanisms by which heat is removed from Venus's 
interior to the surface? Global plate tectonics, like Earth's, are absent on 
the planet (Zharkov 1983; Solomon and Head 1982), although in individual, 
smaller regions, it is possible that there are features of plate tectonics (Head 
and Grumpier 1987). A certain portion of heat may be removed by the 
mechanism of hot spots (Solomon and Head 1982; Morgan and Phillips 


1983). Conductive transport of heat through the crust clearly plays a large 
role. However, with a large crust thickness ( ^ 40 km), as indicated by 
data from a number of works (Zharkov 1983; Anderson 1980; Solomatov et 
al. 1987), the heat flow of F « (40-50) erg cm'^s"^ triggers the melting of 
the lower crust layers and removal of approximately one half of heat flow 
by the melted matter. The latter flows to the surface as lava or congeals in 
the crust as intrusions. 

We shall discuss the possibility of solid-state convection in the crust as 
an alternative mechanism of heat removal through the Venusian crust. 

The crust is constituted of an upper, resilient layer with a thickness of 
de and a viscous one with a thickness of d^ = d^r — d^. 

The crust thickness of d^r is constrained in our model by the phase 
transition of gabbro-eclogite, since eclogite, with a density higher than 
that of the underlying mantle, will sink into the mantle (Anderson 1980; 
Sobolev and Babeiko 1988). The depth of this boundary is dependent 
upon the composition of basalts of Venus' crust. We assume that d^r = 
70 km (Yoder 1976; Zharkov 1983; Sobolev and Babeiko 1988). It is 
considered that radioactive elements are concentrated in the upper portion 
of the crust, and the primary heating occurs via the heat flow from the 
mantle of Fl » 40 erg cm"^s~^ The boundary (d^) of the resilient crust 
is deflned as the surface of the division between the region effectively 
participating in convection and the nonmobile upper layer. Crust rheology 
is described by law (1) with the parameters from Kirby and Kronenberg 
(1987). Four modeled rocks are considered: quartz diorite, anorthosite, 
diabase and albite. Parameter m in (1) is close to 3 for them, so that the 
formulae MAPC with parameters (8) for fixed boundaries is fully suitable 
for estimating. In addition, criterion (15) is used to define the boundary, 
de. At this boundary, which is regarded as the upper boundary of the 
convective portion of the crust, the temperature is equal to 

To = m + 1Qd^{km),K. (38) 

The following physical parameters are assumed (Zharkov et al. 1969): 

p=2.%g cm-^,a = 2\0-^K-\ se = 2 -lO^erg cm-h-'^K-\ 

Computations have demonstrated that the thickness of the resilient 
crust is 20-30 kilometers. The mean temperature of the convective layer 
of the crust has been calculated at ~ 1600K, 1700K, 1900K and 2000K, 
respectively, for quartz diorite, anorthosite, diabase, and albite, and exceeds 
the melting temperature for basalts by hundreds of degrees. This means 
that convection does not protect the crust from melting, and heat is removed 
by the melted matter. 


We can estimate that portion of the heat which is removed by con- 
vection. Fbr this, let us assume the temperature in the base of the crust 
to be Tb = 1500K (approximately the melting temperature). We obtain 
the Nusselt number from the formulae of MAPC, and find that it is ~1.7; 
1; 0.6; and 0.5, respectively, for quartz diorite, anorthosite, diabase, and 
albite. For rj = const, and for complex rheology, as in (1), (Christensen 
1984a and 1985a), convection begins at Nu ^ 1.5-2, as calculated according 
to the formulae of APC (MAPC). Thus, where der « 70km, perhaps only 
quartz diorite is convective, removing 25-30 erg cm~^s~\ while 10-20 erg 
cm~^s~^ is removed by the melt. The rate of convective currents is three 
to five millimeters per year. It can be demonstrated that 

Nu^id,r-d,)°' (39) 

With dcr ~ 120 km, convection also begins in anorthosite, while in 
quartz diorite it occurs virtually without melting. 

These estimates show that convection in the crust may play some role 
in individual regions, depending on the thickness and composition of the 
crust It is not excluded that in individual regions, convection in the crust 
makes its way to the surface. The bulk of the heat is, apparently, removed 
by melted matter. The rate of circulation of material from the crust is, 
with this kind of volcanism, 50-100 km^yr-^ This is three to five times 
greater than crust generation in the terrestrial spreading zones. Another 
process by which basalt material circulates is where new portions of melted 
basalt reach the crust from the upper mantle, and basalt returns back to the 
mantle in the eclogite phase. This process may trigger the accumulation of 
eclogite in the gravitationally stable region between the upper and lower 
mantles. It may lead to the chemical differentiation of the mantle. This 
process has been noted for the Earth by Ringwood and Irifune (1988). 

Figure 4 illustrates various processes involved in heat and mass trans- 

The geological structures observed on Venus may be related to these 
processes. Flat regions may be tied to effusive, basalt volcanism. Linear 
structures in the mountainous regions may be related to horizontal defor- 
mations which are an appearance of convections in the crust or mantle. 
Ring structures may stem from melted intrusion or hot plume lifted towards 
the surface from the bottom of the upper mantle. 

Convection both in the mantle and in the crust is, apparently, nonsta- 
tionary (as on Earth). This nonstationaiy nature stems from instabilities 
occurring in the convective system. The characteristic time scale for such 
fluctuations is t ~ d/u, where d ~ 10^-10^ cm is the characteristic dimension, 
and u ~ 1 cm per year is the characteristic velocity. Therefore, character- 
istic "lifespans" for various occurrences of instability are t ~ 10*-10^ years. 



(a) Cortductiwe heat 

» ♦ ^ 

[d) Lift ol tie mantle plume 

(b) Heat removal by melled matler 

(e) Mande corwectiwi reaches 
the surface 

(cj Convertion in the cnjsl 

^f) Basalt exchange belweefi the 
cfusl and the mantfe 

FIGURE 4 Process of heat transport through the Venusian crust: (a) transfer of heat 
carried from the mantle by the mechanism of conductive thermal conductivity; (b) heat 
removal by the melted matter which is formed as the basalt cnist melts. The melted matter 
may Bow to the surface or form intrusions; (c) convection in the crust which does not 
reach the surface or reaching the surface; (d) lifting of hot plume from the bottom of the 
upper mantle to the crust of Venus, triggering enhanced heat flow, a flow of crust material, 
and the sinking of the crust; (e) involvement of the crust in mantle convection with the 
formation of spreading zones; (f) basalt exchange between the crust and the mantle. Basalt 
is formed when the upper mantle partially melts and is returned back as eclogite. 

Regional features of tectonic structures, thermal flows, volcanic activity and 
so on, can exist for this length of time. 


1. Modification of the approximation of parameterized convection 
for the case of nonNewtonian mantle rheology led to no marked increase 
in the time scale of thermal inertia of the mantle from two to three or three 
to four billion years in comparison with the usual parameterization. The 
thermal flow at the surface of Venus of ~ 50 erg cm~^s"\ is the product 
of radiogenic heat release from the mantle (50%), heat release in the 
crust (20%), and cooling of the planet (30%). These figures for Earth are 
approximately 40, 20, and 40% for the double-layered convection models. 
Tfemperatures in the upper portion of the mantle are approximately 1700 K, 
which is 50-100 K greater than on Earth. Given the existing uncertainties 
in the concerning parameters, T^m ~ 3700-4000 K at the core boundary 
and may, possibly, be greater. This temperature is 100-300 K less than for 
the Earth. 

2. The magnetic field on Venus is absent. This is most likely due to 
the lack of core solidification and, respectively, the lack of energy needed 



to maintain convection in the liquid core. For this, it is enough for the 
sulfur content in Venus' core to be even a little bit less than on the Earth 
(but not more than 20-30% less). This conclusion is stronger if the triple 
point in the phase diagram for iron, 7 - e- 1, lies at pressures that are 
greater than in Venus' center, but approximately less than in Earth's center. 

3. At the values obtained for heat flows from Venus' mantle, the crust 
melts, and the melted matter ( < 100 km^ per year) removes about one half 
of the entire heat. The remainder is removed conductively. In individual 
regions, depending on the crust thickness and composition, a portion of the 
heat may be removed by convection, reducing crust temperature and the 
portion of heat removed by the melted matter. Flow velocities comprise 
several millimeters per year. Due to the insufficiently high temperature of 
the surface, convection in the crust separates from the surface as a highly 
viscous, nonmobile layer with a thickness of 20-30 kilometers. In individual 
regions, crust convection may emerge to the surface. Basalt circulation also 
occurs by another way: the basalt is melted out of the upper mantle and 
returned back in the form of eclogite masses, which sink into the lighter 
mantle rock. It is possible that this process triggers the accumulation of 
eclogite at the boundary between the upper and lower mantles, resulting 
in the chemical separation of the mantle. These processes may explain the 
formation of various geological structures on Venus. 

4. The nonstationary nature of convection in Venus' mantle and crust 
determine regional features of tectonic, thermal and volcanic appearances 
on the surface of the planet which have a characteristic duration of ~ 
10*-10» years. 


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James C.G. Walker 
The University of Michigan 


Measurements of the concentrations of rare gases and trace elements 
in oceanic basalts have provided new information concerning the structure 
of the Earth's mantle and its evolution. This review is based principaUy 
on papers by Allegre, Staudacher, Sarda, O'Nions, Oxburgh, and Jacobsen. 
Approximately 35% of the mantle lost more than 99% of its rare gas 
content in the first 100 million years of solar system history. A comparable 
volume of the mantle has also been depleted in radioactive and other 
large ion lithophile elements, the depleted elements being concentrated in 
continental crust But depletion was a much slower process than degassing. 
The average age of continental crust is 1.8 billion years, but the average age 
of the rare gas atmosphere is 4.4 billion years. There has been very little 
mixing of material between the degassed and depleted porUon (presumably 
the upper mantle) and the undegassed and relatively undepleted portion 
(presumably the lower mantle). 

Gas fluxes from the mantle indicate that degassing today is inefficient, 
affecting only the top few hundred meters of oceanic crust. It is not likely 
that sea floor spreading processes Uke those now operating could have 
degassed the entire upper mantle within a 100 million years, even given 
large initial heat fluxes. At the same time, it is not Ukely that sea floor 
spreading processes could have dissipated the initial heat of a nearly molten 
Earth. Lava flooding could have removed initial heat efficiently and at the 
same time degassed the upper mantle rapidly. 

Rare gases do not make an atmosphere, of course. There is new 
information concerning the release of carbon dioxide from the mantle. As 




pointed out most forcefully by Marty and Jambon, the exogenic system 
(atmosphere, ocean, and sedimentary rocks) is deficient in carbon by a 
factor of 100 relative to rare gases when present amounts are compared 
with present fluxes from the mantle. It appears that carbon dioxide did 
not participate in the initial rapid degassing that released rare gases from 
the upper mantle. Instead, carbon has been modestly concentrated into 
the continental crust like other incompatible, but not atmophile, elements. 
Less than 10% of upper mantle carbon has been uansferred to the crust, 
and the total mantle amount may be 40 times the amount in the exogenic 


Important new information has become available in recent years con- 
cerning the release of gases from the interior of the Earth. The most fruitful 
source of information has been the measurement of rare gas concentrations 
in sea floor basalts. The results set important constraints that need to be 
incorporated into any comprehensive understanding of the early history 
of the planets. In my review here, I will describe some of the highlights 
of these results and give an indication of how they are derived. I cannot 
provide a complete description of all of the evidence that is used to reach 
the conclusions presented. 


Measurements on sea floor basalts have provided clear indications of 
two major reservoirs within the mantle. The larger reservoir, constituting 
about 65% of the mantle, is undegassed and relatively undepleted in 
incompatible elements. The remaining 35% of the mantle was degassed 
very early in Earth history (within 100 million years of the beginning), and 
more than 99% of the initial gas content of this reservoir was released. 
Throughout the whole of Earth history there has been very little mixing 
between these reservoirs (O'Nions 1987; Anderson 1989). 

These conclusions are based on measurements of the concentrations in 
sea floor basalts of the radioactive parent elements shown in Figure 1, along 
with their radiogenic daughter isotopes and non-radiogenic cousin isotopes 
also shown in the figure (Allegre et al. 1983). The important feature of 
these isotope systems is that the ratio of daughter/cousin increases through 
time as a result of the radioactive decay of the parent, and that there are 
no other processes that will cause the ratio of daughter/cousin to change 
because they are chemically and physically almost identical. 

Figure 2 shovre how the ratio of daughter/cousin, called ALPHA, 
increases at a rate that depends on the ratio of parent/cousin, called MU. 


Parent Daughter Cousin 

K40 Ar40 Ar36 
U,Th He4 He3 

1129 Xel29 Xel30 

■ ALPHA (=DAUGHTER/COUSIN) increased by 

■ MU (=PARENT/COUSIN) determines rate of 

FIGURE 1 Isotope taxonomy. 

The solid line in the top panel of the figure shows the evolution of the 
amount of radiogenic ^°Ar resulting from the decay of radioactive ^°K. 
The bottom panel shows the evolution of the ratio of ''"Ar/^^Ar, ALPHA. 
The effect of a degassing episode fairly early in Earth history is indicated 
by the left hand arrow labeled Degas 50%. The degassing episode reduces 
the concentration of ^"Ar by a factor of two, as shown in the top panel. 
Because ^^Ar concentration is also reduced by a factor of two there is 
initiaUy no change in ALPHA The rate of increase of ALPHA with tune 
is larger after the degassing episode, however, because there is less Ar 
in the denominator of the ALPHA ratio. This evolution is shown by the 
dashed Une in the figure. The effect of a second degassing event at -1 biUion 
years is also shown in the figure. The impact of the second degassing event 
on the evolution of ALPHA is smaller because, later in Earth history, 
there is less radioactive ^"K left to decay. Thus, early degassing leads to 
large increases in ALPHA; late degassing has a smaller effect. The event 
in the middle of Figure 2 shows the effect of a depletion by 50% in the 
concentration of radioactive ""K. Depletion reduces the rate of increase 
of ALPHA in the manner indicated by the dashed line. In this way it is 
possible to deduce the history of MU from measurements of ALPHA 

The basic data concerning mantle degassing appear in Figure 3. They 
are ALPHA values measured for He, Ar, and Xe in mid-ocean ridge 
basalts and in ocean island basalts. The mid-ocean ridge basalts appear to 
sample the upper mantle, whereas the ocean island basalts are assumed 





O i) 

1 - 

■S 0.5 H 

I— H 


400 H 


^ 200 




5051^ r 

Degas 50$K 


-3 -1 


FIGURE 2 Measure ALPHA to deduce history of MU. 

to sample plumes of material rising from the lower mantle. There is a 
range of compositions of ocean island basalts representing various degrees 
of mixing between lower mantle material and upper mantle material. As 
representative of the least contaminated material I show results for Loihi 
sea mount in Hawaii. The point is that ALPHA is larger in MORS than in 
Loihi material, which indicates that MORE material is more degassed. The 
enhancement in ALPHA has been large for He and Ar. From data such 
as these it is now possible to derive important results concerning mantle 

First, the bulk Earth concentration of K gives the ''"Ar concentration in 
undegassed mantle material. The ALPHA value observed in Loihi basalts 
gives the ^^Ar concentration in undegassed mantle material. The mass of 
^^Ar in the atmosphere then gives the mass of the mantle that has been 
degassed. From a comprehensive study of rare gas isotope systematics 
Allegre et al. (1987) deduce that 46% of the mantle has been degassed. 
lb increase the ALPHA value of Ar from the Loihi value to the MORE 
value it is necessary that no more than 390/25000 = 1.6% of the initial ^^Ar 
complement be retained in degassed mantle material. This value would 
apply in the case of early degassing from undepleted material. Delayed 
degassing or prior depletion of ''"K would reduce the permitted degree of 



He Ar Xe 

MORE 86,000 25,000 6.95 
Loihi 25,000 390 6.48 

■ MORE samples degassed reservoir 
(upper mantle) 

■ Loihi samples undegassed (lower 

FIGURE 3 Data that constrain degassing (Allegre el al. 1987). 

retention. The conclusion is that degassing has been very thorough indeed. 
At the same time, because the difference between ALPHA values in Loihi 
and MORE is so great, it is possible to conclude that just 2% contamination 
of MORE material by Loihi material would reduce the ALPHA value of 
the degassed mantle by a factor of two. There is therefore evidence for 
strong isolation of the mantle reservoirs from one another. 

The increase in the ALPHA value for Xe between Loihi and MORE, 
although modest, demonstrates that degassing took place very early in 
Earth history. For ALPHA to have changed, degassing must have occurred 
before all of the parent ^""H had decayed away. But the half life of ^^H 
is only 17 million years. Therefore, the division of the mantle into two 
reservoirs, the very thorough degassing of one of these reservoirs, and the 
nearly total isolation of the two reservoirs all took place very early in Earth 
history. At this time it is not clear to me how to reconcile these surprising 
conclusions with our current understanding of the growth of the Earth by 
planetesimal impact, in which planetesimals were vaporized and degassed, 
at least during the later stages of accretion. Neither is it clear how to 
reconcile with these data the current thinking concerning the formation 
of the Moon by a giant impact event occurring near the end of Earth 



accretion. It appears likely that such an impact would have completely 
remixed and homogenized the mantle. On the other hand, it is not clear 
that such an impact event would have led to complete degassing of the 
mantle or to complete removal from the Earth of any atmosphere released 
during the course of previous accretion. Also unclear is what physical 
process causes the separation of the mantle into two distinct reservoirs. In 
my further analysis I shall assume that degassing of the upper mantle was 
a consequence of mantle convection, possibly driven by accretional energy, 
but that most of the impacts, and in particular the giant Moon-forming 
impact had already occurred before the processes that brought about the 
presently observable state had begun. 

In this interpretation then, degassing should be related to continental 
growth and the depletion of the upper mantle in incompatible elements. 
Studies of continental growth and depletion are based on precisely the same 
kind of isotopic arguments as the studies of degassing already described. 
The only difference in depletion is that the daughter and cousin isotopes 
are concentrated in the continents instead of in the atmosphere. Analyses 
of Sm-Nd, Lu-Hf, and Rb-Sr isotopes in sea floor basalts, summarized in 
Figure 4, indicate that 30% of the mantle has been depleted to form the 
continents (Jacobsen 1988). The average age of the continents is 1.8 Ga. 
Allegre et al. (1983, 1988), in a similar analysis, conclude that 35% of the 
mantle has been depleted while 47% of it has been degassed (Sarda et 
al. 1985). The average age of the rare gas atmosphere deduced in their 
analysis is 4.4 Ga. My tentative conclusion is that the degassed and depleted 
reservoirs are probably the same, but that degassing occurred much earlier 
than depletion. 


Fluxes of gases from the mantle to the atmosphere can be deduced 
from the measured flux of ^He and the concentration ratios in sea floor 
basalts. These fluxes lead to the veiy interesting conclusion that heat is 
released much more readily from the mantle than are the rare gasses 
(O'Nions and Oxburgh 1983; Oxburgh and O'Nions 1987). Further it can 
be argued that degassing today is ineflicient. Processes now operating could 
not have degassed the upper mantle rapidly and thoroughly. A comparison 
of the fluxes of heat, helium, and argon is presented in Figure 5. The 
sources are mainly concentrated in the lower mantle because the upper 
mantle is depleted in radioactive incompatible elements. The heat flux 
through the surface of the Earth exceeds the sum of upper and lower 
mantle sources because the interior of the Earth is cooling down. This fact 
is reflected in the Urey ratio of source/flux. For heat this ratio has a value 
of about 0.6 (Pollack 1980). For ^He the Urey ratio is 6.8, indicating that 




' 77777777777 7. 










Allegre et al. 

V/Z//v^ZZ7ZZ ZZZ^^^m^ 

He 3 
He 4 

FIGURE 4 Comparison of deductions concerning degassing and depletion (Allegre a al. 
1983, 1987; Jacobsen 1988). The bars indicate what fraction of the terrestrial complement 
of each isotope is in the indicated reservoir. HEAT Q refers to heal source. 

//y//////// /i^^^^^^^^^^^^im<^ 

^777/ZJZZ7/ 7:7j^Z2^^^^^ 


V 7777^Z ZZZ Z/ZZ7'^^^ 

0.5 10 


most radiogenic helium is retained within the Earth and that the flux from 
mantle to atmosphere is much less than the production within the Earth. 
However, the flux does exceed upper mantle production. Helium must be 
flowing from the lower mantle to the upper mantle at a significant rate. 
For ""Ar, on the other hand, the flux is less than the upper mantle source. 
There is no evidence of flow from lower mantle to upper mantle; the Urey 
ratio is 23, and ''°Ar is accumulating even in the depleted upper mantle. 
These observations provide strong support for the notion of a two-layer 
convective structure in the mantle. 

It is entirely reasonable to suppose that heat is more mobile than 
helium which is in turn more mobile than argon. The argon flux from the 
mantle is 6.2 x 10^ mole^. The ^°Ar concentration in the upper mantle 
is 3 X 10-1° mole/g. Therefore, the rate at which upper mantle material 
is degassed, calculated from the ratio of these two numbers, is 2 x 10*^ 
gy^. Since the mass of the upper mantle (35% of the total mantle) is 1.4 
X 10^'' g, it would take 70 Ga to degas the upper mantle at this rate. But 
the xenon isotope data indicate that the upper mantle was degassed in less 
than .1 Ga. Therefore, the present rate of degassing is too slow to explain 
the observations by a factor of 1000. 

Furthermore, degassing today is inefficient, in the sense illustrated in 
Figure 6. Ocean crust is formed by the partial melting of upper-mantle 




He 4 







FLUX: 3.6E15 A 9.6E7 A .62E7 A 

Upper mantle 


.09E15 4E7 1E7 

watt mole/y 


Lower mantle 





FIGURE 5 Fluxes of heat and gases and ratios of sources to fluxes. 

material. The degree of partial melting can be deduced from the con- 
centrations of the completely incompatible element potassium. Potassium 
concentration is enhanced in ocean crust by a factor of 10, more or less, 
so we have approximately a 10% partial melt of 60 kilometers of upper 
mantle material to produce six kilometers of ocean crust. About the same 
Increase by a factor of 10 can be expected in the concentration of '"'Ar, 
also presumably a completely incompatible element New ocean crust is 
generated at the rate of 3 km^ per year, lb produce the '*°Ar degassing flux 
of 6.2 X 10^ mole per year it would be necessary to extract '"'Ar from just 
the top 250 meters of ocean crust. This extraction presumably occurs by in- 
teraction between sea water and the ocean crust The ''°Ar does not diffuse 
directly out of the crust or bubble out of the magma. It must be extracted 
by leaching at relatively shallow depths in the crust. During the lifetime of 
the sea floor before subduction, heat will be extracted from a lithospheric 
layer approximately 60 kilometers thick, but Ar will be extracted only from 
250 meters of ocean crust This thickness of crust is equivalent, before 
partial meUing, to 15 kilometers of upper mantle, so the release of Ar is 
about 25 times less efficient than the release of heat. The flux data indicate 
that radiogenic rare gases are accumulating in the mantle. The degassing 
process now operating is inefficient and slow. It seems that the process 
that originally degassed the upper mantle completely and rapidly must have 
been markedly different from the process now operating. 





K=42 ppm 



60 km 

Ar40 degassing flux 
= 6.2E6 mole/y 

3 km"2/y 





12250 m 

K=500 ppm 

103S partial melt 

FIGURE 6 Degassing is inefficient compared with the extraction of heat. 


lb what extent can the rare gas results be applied to more important 
constituents of the atmosphere? It turns out that there is significant infor- 
mation concerning carbon dioxide (Des Marais 1985; Marty and Jambon 
1987). The data and results are summarized in Figure 7. The flux of carbon 
dioxide from mantle to atmosphere today is 2 x 10'^ mole per year. The 
flux of ^^Ar is 250 mole per year, so the ratio of the fluxes is 8 x 10^. 
On the other hand, the ratio of the amounts in atmosphere, ocean, and 
continental crust is 1.8 x 10^. The ratio of fluxes is very much larger than 
the ratio of amounts now present in the surface layers of the Earth. Carbon 
is missing from the surface layers relative to argon. 

This conclusion can be seen also in the accumulation times calculated 
by dividing the flux into the amount. Carbon would accumulate at present 
rates in 5 x 10^ years, but it would take 2.2 x 10'^ years for the ^^Ar now 
in the atmosphere to accumulate at the present flux. The conclusion is that 
while ^®Ar was massively degassed earlier in Earth history, carbon did not 
participate in this early degassing. If carbon was rapidly released from the 
mantle early in Earth history it was just as rapidly returned to the mantle. 

Carrying this analysis further it can be concluded that carbon is a 
lithophile and not an atmophile element. From the flux ratio of carbon to 



Accumulation times: 


2.2E13 y 


Ratio C/Ar 

5.6E15 mole 




Fluxes: 2E12 250 mole/y 

Flux ratio C/Ar = 8E9 

FIGURE 7 Compared to argon, carbon is deficient in the crust and atmosphere. 

^^Ar and the concentration of ^^Ar in the upper mantle we can calculate 
the concentration of carbon in the upper mantle. The value is 1 x 10~^ 
mole/g. This calculation assumes that carbon is not more mobile than Ar, 
sarely a reasonable assumption. If carbon is less incompatible than Ar the 
required upper mantle concentration of carbon would be larger. From the 
concentration and the mass of the upper mantle I calculate that there are 
1.4 X 10^^ moles of carbon in the upper mantle. The amount in the crust 
and atmosphere and ocean is only 1 x 10^^ mole (Wilkinson and Walker 
1989). Therefore less than 10% of upper-mantle carbon has been degassed. 
By way of contrast, more than 99% of upper mantle ^® Ar has been degassed. 
Continuing the analysis and assuming that the lower- mantle concentration 
is given by the upper-mantle concentration augmented by crustal carbon 
mixed back in, the total amount of carbon in the mantle is 4.2 x 10^^ 
mole, which is 42 times the amount in crust, ocean, and atmosphere. It 
seems that the fate of most carbon dioxide released from the mantle is 
to be incorporated into oceanic crust in weathering reactions and to be 
carried back into the mantle on subduction. Only a small fraction of the 
carbon is captured in the exogenic system as cratonic carbonate rocks. The 
average carbon concentration in continental crust is 5 x 10* mole/g. The 
concentration in the upper mantle is 1 x 10^ mole/g. Therefore, the crust 
is only moderately enriched in carbon dioxide relative to the upper mantle 
and, unlike the rare gases, carbon is a modestly incompatible element 



The rare gas data indicate that there was early, thorough degassing 
of the upper mantle, but that there remain large amounts of primordial 
rare gases in the undegassed, lower mantle reservoir. The time scales 
and rates of degassing and depletion are very different. Depletion and 
continental growth occurred much later in Earth history than degassing. 
Degassing today, by weathering of the sea floor, is a slow and inefficient 
process and could hardly have provided the rapid and total early degassing 
that apparently occurred. Carbon dioxide did not degas like the rare 
gasses and is only modestly incompatible in the upper mantle. With the 
example of carbon dioxide in mind, we must be cautious about deducing 
degassing histories of other important atmospheric gases like nitrogen or 
water from the rare gas data. In the absence of relevant observations it is 
not immediately clear whether other atmospheric gases have behaved more 
like argon or more like carbon dioxide. By analogy with the Earth, it does 
seem likely that large amounts of both rare gases and carbon dioxide may 
be retained within the interiors of Mars and Venus. This possibility must be 
kept in mind in the study of the origin of planetary atmospheres. I do not 
feel that we yet have a satisfactory description even in quaUtative terms of 
the origin of the Earth and the atmosphere. The challenge is to reconcile 
the ideas of planetary growth by accretion, impact degassing during the 
course of accretion, the origin of the Moon by a giant impact, and the data 
described in this paper concerning the degassing history of the mantle. 


This research was supported in part by the National Aeronautics and 
Space Administration under Grant NAGW-176. I am grateful to Alex 
Halliday and Richard Arculus for guidance and advice. During the course 
of the conference my ideas were significantly influenced by discussions with 
D. Weidenschilling, L. Mukhin, Jim Kasting, Dave Stevenson, and VN. 
Zharkov. I am grateful to all of them. 


Allegre, CJ., S.R. Hart, and J.-F. Minster. 1983. Chemical structure and evolution of 

the mantle and continents determined by inveision of Nd and Sr isotopic data, II. 

Numerical experiments and discussion. Earth Planetary Sd. Letters 66:191-213. 
Allegre, CJ., T Staudacher, P. Sarda, and M. Kurz. 1983. Constraints on evolution of 

Earth's mantle from rare gas systematics. Nature 303:762-766. 
Allegre, CJ., T Staudacher, and P. Sarda. 1987. Rare gas systematics: formation of 

the atmosphere, evolution and structure of the Earth's mantle. Earth Planetary Sci. 

Letters 81:127-150. 
Andenion, D.L. 1989. Composition of the Earth. Science 243: 367-370. 


Des Marais, DJ. 1985. Carbon exchange between the mantle and the cnist and its 

effect upon the atmosphere: today compared to Archean time. Pages 602-611. In: 

Sundquist, E.T, and W.S. Broecker (eds.). Natural Variations in Carbon Dioxide and 

the Carbon Cycle. American Geophysical Union, 'Washington, D. C 
Jaa>bsen, S.B. 1988. Isotopic and chemical constraints on mantle-crust evolution. Geochim. 

CoMuochim. Acta 52: 1341-1350. 
Marty, B., and A. Jambon. 1987. C/^He in volatile fluxes from the solid Earth: implications 

for carbon geodynamics. Earth Planetary Sd. Letters 83:16-26. 
Oxburgh, E.R., and R.K. O'Nions. 1987. Helium loss, tectonics, and the terrestrial helium 

budget. Science 237:1583-1588. 
O'Nions, R.K., and E.R. Oxburgh. 1983. Relationships between chemical and oonvective 

layering in the Earth. J. Geological Soc London 144:259-274. 
O'Nions, R.K., and E.R. Oxburgh. 1983. Heat and helium in the Earth. Nature 306:429-431. 
Pollack, H.N. 1^0. The heat flow from the Earth: a review. Pages 183-192. In: Davies, 

P.A., and S.K. Runcorn (eds.). Mechanisms of Continental Drift and Plate Tfectonics. 

Academic Press, New York. 
Satda, P., T. Staudacher, and CJ. Allegre. 1985. *°M^At in MORB glasses; constraints 

on atmosphere and mantle evolution. Earth Planetary Sd. Letters 72:357-375. 
Wilkinson, B.H., and J.CG. IMilker. 1989. Phanerozoic cycling of sedimentary carbonate. 

American J. Sci. 289:525-548. 

NQ1 -22975 

The Role of Impacting Processes in the 

Chemical Evolution of the 

Atmosphere of Primordial Earth 

Lev M. Mukhin and M.V. Gerasimov 
Institute of Space Research 


The stability of the chemical composition of the planets' atmospheres 
on any time scale is determined by the ratio of source and sink strengths for 
various atmospheric constituents. Beginning with the Earth's formation and 
continuing throughout its history, these ratios have undergone significant 
alterations. Such changes are determined by various physical processes that 
are tied to the evolution of the Earth as a planet. A complete theory of the 
origin and evolution of the Earth's atmosphere is still far from complete 
at this time. This is due, in particular, to a certain randomness in the 
selection of a number of important physical parameters of the preplanetary 
cloud. They include, for example, the time scale for the dissipation of the 
gaseous nebula component; the planet accretion scale; and the chemical 
composition and distribution by size of planetesimals. It will therefore be 
useful to consider some physical constraints on the process by which the 
Earth's atmosphere was formed. 

Currently existing paleontological data offer clear evidence of the 
presence of life on Earth 3.5 billion years ago (Schopf and Packer 1987). 
Furthermore, we can make the fundamental conclusion from the analysis 
of carbon isotope ratios '^C/^^C that an almost contemporary biogeochem- 
ical carbon cycle (Schidlowski 1988) existed on Earth 3.8 billion years ago. 
Moreover, there is some reason to believe that this last dating could be 
pushed further back to four billion years (Schidlowski, personal communi- 
cation). There is no doubt that both the prebiological evolution processes 
and the global biogeochemical carbon cycle can only occur in a sufficiently 



dense atmosphere and hydrosphere that have ah-eady formed or are form- 
ing. Taking into account data from isotope systematics (F^ure 1986), with 
which we can estimate the Earth's age at 4.55 to 4.57 billion years old, we 
conclude that the time scale for prebiological evolution and the emergence 
of life on Earth was sufficiently brief: possibly less than 0.5 billion years. 
This fact means, however, that the Earth's protoatmosphere must have 
been formed prior to the appearance of the biogeochemical cycle, that is, 
over a period of time significantly less than 0.5 billion years. Additional 
indirect evidence of the early emergence of the Earth's atmosphere can be 
found in analyzing the isotope relationships of the noble gases Ar and Xe 
(Ozima and Kudo 1972; Ozima 1975; Kuroda and Crouch 1%2; Kuroda 
and Manuel 1962; Phinney et al. 1978). 

Therefore, existing and observed data provide evidence of the very 
early formation of a dense atmosphere on Earth. We shall consider possible 
scenarios for the formation of the Earth's early atmosphere and its initial 
chemical composition. 


A model for Earth's early atmosphere, formed from solar composi- 
tion gas captured gravitationally during the final stages of accretion, was 
explored in Hayashi's studies (1981, 1985). Hydrogen and helium are the 
primary components of this atmosphere. According to the estimates of 
several authors, the total mass of the initial atmosphere could have reached 
1026.1031 g (Hayashi et al. 1985; Cameron and Pine 1973; Lewis and Prinn 
1989). However, the inference by these models that the entrapment pro- 
cess occurred isothermically may lead to significant error: they overlook 
the heating up of the gas during accretion (Lewis and Priim 1984). We will 
note that there are some additional difficulties in a model of an isothermal, 
initial atmosphere. They stem from the diffusive concentration of heavy 
gases in the initial atmosphere (Walker 1982). The pressure of the initial 
atmosphere for Earth is only 0.1 bar in the more realistic models of the 
adiabatic, gravitational capture of gas from a protoplanetary nebula (Lewis 
and Prinn 1984). 

Clearly, an initial atmosphere could only have formed if the processes 
of gas dissipation from the protoplanetary nebula had not ceased by the time 
Earth's accumulation had concluded. Gas dissipation from a protoplanetary 
nebula is determined by a solar wind from a young T Tkuri Sun and EUV 
(Sekiya et al. 1980, Zahnle and ^^^lker 1982; Ehnegreen 1978; Horedt 
1978;). Canuto et al. (1983) have estimated the time scale for dissipation 
of the gaseous component of a protoplanetary nebula, using observed data 
on T Tliuri star luminosity. Their estimates show that this time scale is not 
more than 10'' years. It may only be several million years, beginning with 


the onset of the convective phase in the history the Sun's development. This 
time scale is appreciably shorter than the approximately 10* years estimated 
for Earth's accumulation (Safronov 1%9; WetheriU 1980). Hence, current 
theories of stellar evolution, coupled with observed astronomical data, raise 
the possibility that only a very weak initial atmosphere existed at the very 
inception of planets' accumulation process. This is a very serious argument 
against the formation of an initial atmosphere on Earth as proposed by 

Nevertheless, one should note that the accuracy of estimates of the time 
scales for a significant portion of cosmogonic processes at the early stages of 
protosolar nebula evolution is not reliable enough to rule out, with absolute 
certainty, the possibility that an appreciable initial atmosphere existed 
on Earth. According to this scenario, the initial atmosphere encounters 
considerable additional difficulties stemming from its chemical composition. 
Adopting, again, the adiabatic model of the gravitational capture of gas 
from a protoplanetary nebula (Lewis and Prinn 1984), we can see that 
with a 0.1 bar value of the pressure of the primordial atmosphere, the 
nitrogen levels in it would be l(fi times lower than present levels. At the 
same time, neon levels would exceed current neon atmospheric levels by 
approximately 40 times. Walker's more detailed computations, where he 
accounts for the radiative-convective structure of the primordial atmosphere 
(1982), also show an inconsequential pressure for this kind of atmosphere 
at the surface (approximately 0.2 bars). This means that arguments raised 
by Lewis and Prinn (1984) against a primordial atmosphere remain valid 
in this instance. Hence, various scenarios for a dense initial atmosphere 
appear to be highly improbable for the above reasons. Therefore, the very 
rapid formation of a dense Earth atmosphere was apparently a function of 
different physical processes. 


One of the suggested mechanisms for the rapid formation of the 
atmosphere is the intense, continuous degassing of Earth in the conven- 
tional sense of this term, including magmatic differentiation and volcanism 
(Walker 1977; Fanale 1971). There is still no answer to the question 
of whether continuous degassing of the Earth could have been intensive 
enough to allow for the formation of the atmosphere and the hydrosphere 
over a very short time span (< 10* years). Such a possibility exists where 
there is a strong, overall heating of the planet during its accretion. However, 
this entails the inclusion of a number of additional inferences regarding a 
very brief accretion scale: < 5 x 10^ years (Hanks and Anderson 1969). 

Walker's recent analysis of the process of continuous degassing (Walker, 
this volume) shows that the present rate of degassing is clearly insufficient 


to be responsible for forming the atmosphere in a very brief time scale. At 
the same time, biker's proposed numerical estimate of the accumulation 
rale of hot lava on primordial Earth, which could have provided for the 
necessary intensity of degassing (1.3 x 10'^ g^). appears to be unjustifiably 
high. Such intensive volcanism infers that ~ 1.3 x 10^^ g of magma would 
pour out over 10* years of accumulation on the surface, or a quarter of the 
entire present mass of the Earth. 

Under the currentfy adopted planetary accumulation models with an 
approximate 10* year time scale, such a hypothesis would only be justified 
in the case of a gigantic impact (Kipp and Melosh 1986; Wetherill 1986). 
There is no question that a considerable portion of the planet would have 
melted as a result of a gigantic impact which would have released a huge 
quantity of gases. This amount would have been sufficient to have formed 
an atmosphere. Yet, there is no detailed, physical-chemical model of this 
process at the present time. Furthermore, it cannot be considered that the 
very fact of a giant impact in the Earth's history has been firmly established. 
Clearly, if such a catastrophic event did actually take place in the earliest 
history of our planet, its consequences would have been so great that they 
would have been reflected in the geochemical "records." However, the 
scenario explored by Walker (this volume) of two reservoirs of volatiles, 
one of which is virtually entirely degassed (the upper mantle), and the 
other which has conserved its store of volatiles (lower mantle), is difficult 
to reconcile with the idea of a gigantic impact TVuly, such a clear separation 
of the two mantle reservoirs, whose presence has been determined with 
sufficient certainty from observed data (Allegre et al. 1987) is difficult to 
expect in the case of a gigantic impact An attempt should be made to 
analyze the possible geochemical consequences of a gigantic impact and 
reconcile them with existing data. For now, a gigantic impact remains 
a reality only in computational models of the evolution of preplanetaiy 
swarms of bodies. However, this episode is only a specific case of the 
impact-induced degassing of matter. Yet impact-induced degassing was, 
apparently, a determining physical process which led to the very rapid 
formation of protoEarth's atmosphere. 


The role of impact processes in forming Earth's protoatmosphere was 
discussed more than 20 years ago in Florenslqr's study (1%5). During 
the years that followed, this idea was developed in a number of studies 
(Arrhenius el al. 1974; Benlow and Meadows 1977; Gerasimov and Mukhin 
1979; Lang and Ahrens 1982; Gerasimov et al. 1985). Impact-induced 
degassing is rooted in the idea of Earth accumulation from large solids. This 
idea does not require the inclusion of any serious additional proposals. It is 



this circumstance that brings us to the conclusion that impact degassing was 
a real mechanism in the formation of Earth's atmosphere and hydrosphere. 
Departing from the gigantic impact issue, we can see that the maximum 
dimension of those bodies which regularly fell on the planet, and from which 
Earth was formed, could have attained hundreds of kilometers (Safronov 
1%9). These dimensions fit with estimates of the diameters of impacting 
bodies which formed the largest craters on the terrestrial planets and their 
satelUtes (O'Keef and Ahrens 1977). The velocity of the collision of a 
random body of a preplanetary swarm with the embryo of primordial Earth 
is no less than the escape velocity. Therefore, the range of velocities of 
planetesimal collision with a growing planet embryo varies from meters per 
second at the initial stages of its expansion, to > 12 kilometers per second 
at the final stages of accumulation. In reaUty, collision velocities could have 
been significantly higher in the case of a collision between Earth and bodies 
escaping from the asteroid belt, or with comets. In this case, when the mass 
of an expanding Earth reached approximately 10% of its current mass, the 
escape velocity became equal to roughly five kilometers per second; the 
melting of silicate matter began during a collision between planetesimals 
and an embryonic planet (Ahrens and O'Keef 1972). Beginning with the 
point where the mass of the embryo was equal to approximately 0.5 of the 
mass of present-day Earth, impact processes were paralleled by the partial 
vaporization of siUcates (Ahrens and O'Keef 1972). The more high-speed 
planetesimals, reaching a speed of more than 16-20 kilometers per second, 
were completely vaporized. Several works (Ahrens and O'Keef 1972; Gault 
and Heitowit 1963; McQueen et al. 1973; Gerasimov 1979; O'Keef and 
Ahrens 1977) analyze in detail the physics of how colliding matter is heated 
as a shock wave passes through that matter and estimate the efficiency of 
impact-induced degassing. They demonstrate that impact degassing is most 
efficient when melting and partial vaporization of silicate matter begin. It is 
worth noting that the release of the primary volatile components begins long 
before the point when the planet's accumulation process reaches collision 
velocities corresponding to the melting point of matter. Pioneering works 
(Lang and Ahrens 1982, 1983; Katra et d. 1983) establish the beginning 
of volatile loss at extremely low collision velocities of approximately one 
kilometer per second. Using the Merchison meteorite as an example, the 
authors established that about 90% of the initial amount of volatiles is 
already lost at a collision velocity of 1.67 kilometers per second (Tbburczy 
et al. 1986). This loss is due to breakdown of the meteorite's water-, 
carbon-, and sulphur-containing minerals at impact. These experiments 
are proof of the beginning of volatile release at a very early stage of the 
Earth's accumulation. Its mass was less than 0.01 of its final mass. Water 
and carbon dioxide are the main constituents involved in the processes of 
shock-induced dehydration and decarbonatization of minerals. 


As the mass of the embryonic planet increases, escape velocity rises. 
Consequently, there is also a rise in the velocity at which planetesimals 
fall. There occurs a corresponding increase in the heating of matter of the 
planetesimal and the surface of the planet in the central shock zone. The 
nature of degassing processes undergoes qualitative changes. The shock 
process becomes a considerably high-temperature one. Chemical reactions 
occurring in the vaporized cloud become increasingly significant. High- 
temperature chemical processes begin to play a predominant role during 
the final stages of Earth's accumulation, instead of the relatively simple 
processes involved in the breakdown of water-containing compounds and 
carbonates. Colliding matter undergoes total meltdown in the central zone 
of impact at collision velocities of five to eight kilometers per second: 
volatile components are released from the melted matter and interact with 
it. The chemical composition of the released gases must correspond to the 
volcanic gases for magma of corresponding composition and temperature. 
CO2, H2O, and SO2 will clearly be the primary components in such a gas 
mixture. The gases CO, H2, H2S, CH4, and others may be competitors to 
these components, depending on the extent to which planetesimal matter 
is reduced (Holland 1964). Where collision velocities exceed eight to nine 
kilometers per second, vaporization at impact of a portion of planetesimal 
matter becomes significant. 

\^porization of silicate matter is supported by thermodissociation of 
planetesimal mineral constituents. As a result of this process, a considerable 
quantity of molecular and monatomic oxygen is released to the cloud of 
vaporized matter. Melt-vapor equUibrium determines the conditions for 
vaporization. The characteristic vaporization temperature for silicates is 
approximately 3000-5000 K. Vapor pressure is approximately 1-100 bars 
(Bobrovskiy et al. 1974). In these conditions, thermodynamic equilibrium 
in a gaseous phase is reached over a time scale ichtm < 10"^ seconds 
(Gerasimov et al. 1985). Therefore, when large-scale impact episodes 
occur, where the characteristic time scale for the expansion of a cloud of 
vaporized matter tcool is counted in seconds, thermodynamic equilibrium 
(tcooi > hhem) is clearly reached at the initial stage of the expansion 
of such a cloud. Consequently, gases are formed in the cloud from the 
entire range of volatile elements present, regardless of what form they 
displayed in the initial matter. In such conditions, H2O and CO2 will 
be formed inside the dense, hot cloud if hydrogen, carbon, and oxygen 
are present in it. This will occur regardless of the initial presence in 
the planetesimals of carbonates and hydrated minerals. At the same time, 
where carbonates and hydrated minerals are present in planetesimals, a 
portion of the hydrogen and carbon in these minerals will be used to form 
other hydrogen- and carbon-containing components. Less H2O and CO2 
will be produced than with the simple thermal breakdown of minerals. As 




the vapor-gas cloud expands, its density and temperature drop, and Xch 
increases. The expansion process commences when x^„oi ~ ichem- This is 
the point where the reaction products undergo chemical hardening, since 
the time scale for chemical reactions becomes greater than the characteristic 
time scale for cloud expansion as the cloud expands further. Gases with a 
chemical composition corresponding to the moment of hardening are mixed 
with atmospheric gases, interacting with both these gases and bedrock from 
the uppermost layers of the planet (regolith). If the atmosphere is dense, 
mixing of gases in an expanding cloud with atmospheric gases may occur 
earlier, when overall pressure of the expanding cloud pv2/2 + P (p = 
density, v = mass velocity, P = pressure in the vapor-gas cloud) becomes 
approximately the pressure in the atmosphere. The portion of the vaporized 
silicate matter a, which is condensed in the cloud by the time constituents 
harden (occurring at a given temperature T*), is defined by the simple ratio 
(Anisimov et al. 1970): 


where To denotes temperature in the vaporized cloud as it begins to expand. 
Estimates demonstrate that for impact of a planetesimal with a dimension 
of approximately 100 kilometers, the value is T* ~ 2000 K. Therefore, for 
a vaporization temperature of T^ ~ 5000 K, the value is a ~ 60%. This 
means that approximately one half of molecular and monatomic oxygen, 
comprising ~ 30% of the cloud's pressure, (Gerasimov et al. 1985) will 
be released into the atmosphere with each impact. Clearly, the impact- 
vaporization mechanism is a powerful source of free oxygen in Earth's 
earUest atmosphere. 

The chemistry of a high-temperature, gas-vapor cloud is too complex 
to be able to judge it solely in terms of the thermodynamical equilibrium 
in its gaseous phase. Condensation of silicate particles and catalytic ac- 
tivity occur during expansion and cooling of the vaporized cloud. These 
processes can significantly alter the equilibrious gas chemical composition. 
This circumstance imposes certain requirements on the search for both 
theoretical and experimental approaches to the study of chemical processes 
in a cloud of impact-vaporized matter. 

Studies (Gerasimov et al. 1984; Gerasimov and Mukhin 1984; Gerasi- 
mov et al. 1987) used laser radiation to examine the chemical composition 
of gases which form during high-temperature, pulse-induced vaporization 
of the Earth's rockbed and meteorites. They demonstrated that molecular 
oxygen is actually the most abundant constituent in a cloud of vaporized 
matter (Gerasimov et al. 1987), and that it determines the chemical pro- 
cesses occurring in the cloud. Regardless of how reduced the initial matter 
is, the primary volatile elements H, C, and S are released as oxides: H2O, 


CO, CO2 (CO/CO2 > 1), and SO2. In addition to the oxides, a certain 
amount of reduced components and organic molecules is formed in the 
cloud: H2, H2S, CS2, COS, HCN, saturated, unsaturated, and aromatic 
hydrocarbons from CH4 to Q and CH2CHO. Molecular nitrogen is re- 
leased. The vaporization-induced gaseous mixtures for samples belonging 
to both crust and mantle rock, as well as for conventional and carbonaceous 
chondrite, are qualitatively homogenous. This is seen in the preponder- 
ant formation of oxides, and in both the comparable (within one order 
of magnitude) ratios of the gases CO/CO2 and the correlation between 
the various hydrocarbons. The gas mixtures formed at high temperatures 
are in nonequilibrium for normal conditions. Therefore, their chemical 
composition will be easily transformed under the impact of various energy 

One should note that the passage of a planetesimal through the atmo- 
sphere exerts a substantial influence on the formation of the atmosphere's 
chemical composition. Studies (Fegly et al. 1986; Prinn and Fegley 1987; 
Fegley and Prinn 1989) have analyzed this issue in the greatest detail 
in recent years. In the physics of the process, a body of large dimen- 
sion (approximately 10 kilometers in diameter) passes through primordial 
Earth's atmosphere at a speed of approximately 20 kilometers per second; 
shock waves send a large amount of energy into the atmosphere. If we 
put the planetesimal density at ~ 3 g/cm^ (which matches the chondrite 
composition), and the angle of entry into the atmosphere at 45", as first 
approximation, we would have 2.2 x lO^'' ergs. This figure is 0.07% of 
the energy of an asteroid. The energy passes directly into the atmosphere 
as the body flies through, and even more energy (~ 3.2 x 10^^ ergs) is 
"pumped" into the atmosphere by a supersonic discharge of matter from 
the impact crater (Fegley and Prinn 1989). The shock wave front (formed in 
the atmosphere during this process) compresses and heats the atmospheric 
gas to several thousand degrees Kelvin. It is clear that various thermo- 
chemical and plasmochemical reactions are occurring in this region. Due 
to recombination processes, new compounds are formed as cooling occurs. 
This substantially alters the initial chemical composition of the atmosphere. 

We can estimate the chemical composition of the gas mixtures at high 
temperatures, using the standard methods of thermodynamical equilibrium 
(given the presupposition that the time scale for the breakdown of a given 
molecule is less than the time required to cool the elementary gas exchange. 
The most detailed computations of these processes were made in the studies 
of Fegley et al. (1986) and Fegley and Prinn (1989). It seems obvious 
that these findings must be critically dependent on the initial chemical 
composition of an unperturbed atmosphere. The atomic ratio C/O is an 
important parameter here: it determines the "oxidized" and "reduced" 
state of the atmosphere. Fegley and Prinn (1989) demonstrated that if 


C/O > 1 (reduced atmosphere), precursors of biomolecules, such as HCN 
and H2CO, are formed as the asteroid passes through this atmosphere. 
Nitrogen oxides appear in the oxidized atmosphere instead of prussic acid, 
supporting the formation of nitric acid if rain falls. Fegley and Prinn 
(1989) considered several possible chemical compositions for unperturbed 
atmospheres, and they calculated the commensurate alterations in the 
composition owing to the passage of large bodies through the atmosphere. 
I would like to make the following comment regarding their work. The 
authors used computation methods employed for purely gaseous reactions. 
Heterogeneous catalysis on mineral particles (present in the atmosphere 
during the impact-induced discharge of matter) must play a significant role 
in the actual natural process. Heterophase reactions must considerably af- 
fect the evolution of the atmosphere's chemical composition during impact 
reprocessing. However, it is quite difficult to account for these reactions at 
this time. An account of the fluxes of such important components as prussic 
acid and formaldehyde is an unquestionable achievement in the work of 
Fegley and Prinn. Their efforts made it possible to estimate the stationary 
concentrations of these components in a modeled early atmosphere. We 
shall note that the numerical values of the strength of the source of cyanic 
hydrogen formation in atmospheric reprocessing and in experiments on 
laser modeling of the processes of shock-induced vaporization are compa- 
rable (Mukhin et al. 1989). Hydrocarbon and aldehyde output in the latter 
case is significantly higher. 


Gas fluxes from the atmosphere present one of the most difficult 
issues related to the early evolution of the Earth's atmosphere. There 
are no accurate estimates at this time of the reverse fluxes of released 
gases to the surface rock of the young planet It is therefore impossible 
to reliably estimate the stationary concentrations of these gases in the 

The strength of a shock source of atmospheric gases is so great that the 
atmospheric accumulation of gases released during the fall of planetesimals 
at the early stage of accretion would create a massive atmosphere from 
water vapors. A runaway greenhouse effect would develop. Such a scenario 
was developed in several studies (Abe and Matsui 1985; Matsui and Abe 
1986; Zahnle et al. 1988). The massive atmosphere "locks in" heat released 
by the impact. This in turn triggers the heating of the atmosphere and 
melting of the upper layers of the planet's silicate envelope. Zahnle et d. 
(1988) have estimated that the massive water atmosphere should condense 
and form an ocean as planetesimals cease falling. The problem however. 


requires that all atmospheric components be taken into account, particu- 
larly CO2 and SO2. These gases could also support a greenhouse effect, 
making it irreversible under the effects of solar radiation alone. The au- 
thors considered the processes of water dissolution in magma and thermal 
volatization as examples of fluxes for water vapors. Lang and Ahrens (1982) 
looked at the hydration reactions of phorsterite and enstatite transported 
by planetesimals in order to determine H2O flux rates. It should be noted 
that other flux mechanisms may be significant for primordial Earth. 

An actualistic approach to the problem of fluxes is not entirely justified, 
lb assess flux rates it is necessary to take into account physical-chemical 
conditions which correspond to the period of accumulation. One of the 
significant factors for the outflow of atmospheric gases to the regoUth 
is the formation of a large quantity of condensed silicate particles from 
planetesimal matter vaporized during impact. With collision velocities of 
approximately 12 kilometers per second, approximately 30% of the matter 
in the central zone of impact is vaporized (Gerasimov 1979). Particle 
condensation takes place as the vaporized cloud expands and cools. These 
particles of small dimensions are discharged into the atmosphere, settle 
there, and faU to the surface of the accreting planet. Jakosky and Ahrens 
(1979) estimated rates of flux from the atmosphere for water vapor to 
a meter layer of regolith consisting of approximately 50 micron particles. 
Comparison of the rates at which water is released into the atmosphere 
during impact-induced degassing and absorbed by regolith has yielded a 
value approximately 0.008 bars for equihbrium pressure of water vapor in 
the atmosphere. This means that virtually aU of the released water flows 
into the regolith. A similar view was put forward by Sleep and Langan 

A structural-chemical analysis of condensed particles forming in model 
laser experiments (Gerasimov et al. 1988) has demonstrated that the con- 
densed matter is nonequilibrious to a significantly great degree. It concur- 
rently has phases with a high degree of silicon-oxygen tetrahedron (quartz 
type) polymerization and ostrov-type phases. It also includes silicon phases 
with an intermediary degree of Si^"*" oxidation and metal silicon Si". The 
condensed matter primarily contains oxidized iron FeO, as well as metal 
iron Fe". These facts are possible evidence of high chemical activity of the 
condensed particles which form planets' regolith during accumulation. A 
number of experiments iUustrate that the condensed particles in contact 
with water during heating may easily form laminated silicates that absorb 
appreciable quantities of water (Nuth et al. 1986; Nelson et al. 1987). 
Chemically active atmospheric gas components may also react with such 
regolith particles and have flux rates that are significantly higher than on 
present-day Earth with its oxidized crust. 

The rapid (not more than a few seconds) and virtually complete 


absorption by condensed particles of oxygen released during vaporization is 
an important experimental finding (Gerasimov 1987). This is evidence that, 
despite the impact-induced release of large amounts of oxygen into the 
atmosphere, molecular oxygen was absent in the primordial atmosphere: 
it was almost instantaneously absorbed by the regolith. It is possible 
that the same fate (albeit with greater time scales) is also characteristic 
for other chemically active gases. In the future, absorbed gases will be 
repeatedly released into the atmosphere owing to shock-induced processing 
of planet surface matter by falling planetesimals. Chemically inert gases, 
such as the noble gases and molecular nitrogen, may have accumulated 
in the protoatmosphere. Therefore, the degassing fate of noble gases and 
chemically active gases may have been entirely different (Gerasimov et al. 

If we extrapolate the conditions on earliest Earth to the following 
period of "continuous" degassing, with a weaker source of atmospheric 
gases, atmospheric density would have been extremely small. This is due to 
the conservation of high flux rates. The appearance of a volatile-enriched 
(particularly oxygen) protocrust is one of the most important conditions 
for atmospheric stabilization. The appearance of an acidified protocrust 
ensures low flux rates for the majority of atmospheric gases and the accu- 
mulation of an ocean. In turn, the formation of an ocean also governs the 
composition and density of the atmosphere. The appearance of a protocrust 
is currently being considered in models of magmatic differentiation (Ikylor 
and McLennan 1985). The earlier appearance of a protocrust in this model 
runs up against the same difficulties as the catastrophic formation of an 
atmosphere in the continuous degassing model. One possible avenue for 
the appearance of a protocrust is shock-induced differentiation (Mukhin 
el al. 1979; Gerasimov et al. 1985), as a result of which the atmosphere 
and the protocrust are formed within the same process of accumulation. 
However, the question of shock differentiation has yet to be theoretically 
analyzed in-depth and requires additional investigation. 

The shock-degassing source was operative virtually throughout the 
planets' entire accumulation process. The formation of a sufficiently dense 
atmosphere at the earlier stages of accumulation of the Earth and the 
terrestrial planets is problematic owing to the possible rapid flux of atmo- 
spheric components to the regolith. Other factors also had an effect, such 
as shock-induced "cratering" of the atmosphere (Walker 1986), intensive 
T Tliuri-like solar wind, EUV, and thermal volatilization. The probability 
of the formation of a dense atmosphere increases with the accumulation 
of the planet's mass, since by the time accretion is completed there is not 
likely to be any action of intensive solar wind and EUY The loss of gases 
from a planet with a large gravitating mass is also difficult. Uncertainties in 
estimating the density of an impact-generated atmosphere at the final stage 


of accretion are largely related to uncertainties in estimating the rates at 
which gases flow into the regolith. 

Therefore, impact-induced degassing, despite the possible parallel in- 
put of an accretive source and a continuous degassing source was clearly 
the most probable and important source of atmospheric gases during the 
earliest epoch of the Earth's evolution: the period of its accumulation. 
Achievements made in recent years in investigating the impact source allow 
us to assess its strength and the chemical composition of the gases that were 
released. Nevertheless, the question of the evolution of the composition 
and density of the impact-generated atmosphere continues to remain an 
open one, primarily due to ambiguities in estimating gas flux rates from the 
atmosphere during accumulation. Therefore, it is our view that fluxes are 
one of the most important issues pertaining to the origin of Earth's earliest 


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N91-22976 J 

Lithospheric and Atmospheric 
Interaction on the Planet Venus 

Vladislav P. Volkov 
VI. Vernadskiy Institute of Geochemistry and Analytical Chemistry 


A host of interesting problems related to the probability of a global 
process of chemical interaction of the Venusian atmosphere with that 
planet's surface material has emerged in the wake of flights by the Soviet 
space probes, "Venera-4, -5, -6, and -7" (1967-70). It was disclosed during 
tiiese flights that the temperature of Venus' surface attains 750 K, pressure 
is approximately 90 atm., and CO2 constitutes 97% of the atmosphere. We 
shall explore several of these issues which were discussed in the pioneering 
works of Mueller (1963, 1969) and Lewis (1968, 1970): 

• Is Venus' troposphere in a state of chemical equilibrium? 

• Can we assume that the chemical composition of the troposphere 
is buffered by the minerals of surface rock? 

• What are the scales and mechanisms involved as exogenic processes 
take place? 

• lb what degree is the composition of cloud particles tied to the 
process of lithospheric-atmospheric interaction? 

We have succeeded in resolving a number of these problems over 
the past 20 years. At the same time, critical issues such as the chemical 
constituents of the near-surface layer of Venus' atmosphere, cloud particle 
chemistry, and the mineralogy of iron and sulfur in surface rock obviously 
cannot be definitely resolved until further landing craft will have been sent 
to the surface of Venus. 

Several research projects have been conducted in the USSR and the 
United States, which used physical-chemical and thermodynamic methods 



for computing multi-component systems. These projects have helped us to 
understand the particularity of the natural process occurring on the surface 
of Venus (Lewis and Kreimendahl 1980; Barsukov et al. 1980; Volkov et al. 
1986; and Zolotov 1985). 

Factual material from the studies of the atmosphere and surface of 
Venus, gathered with the "Venera" series spacecraft and during the "Pioneer 
Venus" mission, can be used to compare our view of the distribution, 
chemical composition, and physical properties of products of lithospheric- 
atmospheric interaction on Venus. 


The following conclusions on the nature and scope of exogenic pro- 
cesses were made after the probes "Venera-15" and "Venera-16" finished 
mapping Venus: 

• The present surface relief of Venus was formed as a result of the 
combined processes of crater formation, volcanism, and tectonic activity; 

• The rate of renewal of Venus' relief is estimated to take a million 
years for the first several centimeters (in the last three billion years), as 
compared to hundreds of meters on Earth and the first several meters on 
Mars (Nikolaeva et al. 1986); 

• There is no evidence of exogenic processes on a global scale, such 
as lunar regolith; 

• There are no traces of fluvial or aeolian processes having occurred 
on a scale that matches the resolution of the radar images (one kilometer). 

At the same time, microscale exogenic processes have been quite clearly 
manifested. TV-panoramas from "Venera-9" and "Venera-10" recorded 
three types of processes: the formation of cracks; degradation with the 
emergence of desert aeolian weathering ridges; and corrosion, akin to 
porous aeolian or chemical weathering. The "Venera-13" and "Venera-14" 
images show laminated formations which have been interpreted (Floren- 
skiy et al. 1982) as aeolian-sedimentation rock. Their formation can be 
described as a cycle: weathering— transport— deposition— lithiphication— 

weathering. . . 

Experiments to estimate such physical properties of surface rock on 
Venus as porosity, and carrying capacity such as "Venera-13" and "Venera- 
14" (Kemurdgian et al. 1983) confirmed the existence of loose, porous 
bedrock. Loose, porous bedrock with an estimated thickness of 10 cen- 
timeters exists at the landing site of the Soviet "Venera-13" and "Venera-14" 
probes. The question of their geological nature is still unanswered: Are 
they products of chemical weathering or aeolian activity? 


There is no direct evidence of the existence of aeolian forms as yet. No 
global aeolian, martian-type structures were revealed in the area mapped 
by the radars of the "Venera-15" and"Venera-16" probes. Nor do any of 
the four TV-panoramas show aeolian forms. 

Experimental simulation (Greely et al. 1984) demonstrated that in 
an atmosphere of CO2, with a pressure of approximately 100 aim. and 
wind speed of up to 3 m/sec"\ signs of rippling occur when saltation of 
particles of up to 75 /^m in diameter takes place. Theoretical estimates 
of the threshold rates of the separation of particles of varying dimensions 
produced similar results. Dust fraction, transported as suspension, will have 
a diameter of < 30 ^m. 

Scrupulous investigation of the TV-panoramas, incorporating data 
from measurements of the optical properties of the near-surface atmo- 
sphere, have demonstrated that the formation of dust clouds from the 
aerodynamic landing of Soviet probes is a reality. It is considered that the 
nature of particle behavior during wind activity on Venus is similar to the 
sorting of material at the bottom of the ocean at a depth of about 1000 

Let us sum up the information on exogenic processes that was gen- 
erated by research on the morphology and properties of the surface of 

• The rate of exogenic processing of the Venusian surface relief is 
extremely low; the morphology of the ancient (0.5 to one billion years) 
relief has been excellently preserved; 

• physical weathering (the equivalent of terrestrial, geological pro- 
cesses) has not been found: there is no aqueous water, living matter, or 
climatic contrasts; 

• Regolith-like forms of relief are not developed; 

• Aeolian activity on present-day Venus does not lead to the forma- 
tion of global forms which can be differentiated on radar maps; 

• The television images show traces of chemical weathering in the 
form of rock corrosion and degradation. 

TTie findings from X-ray-fluorescent analyses on the Soviet "Venera- 
13" and "Venera-14" and "Vega-2" probes and K, U, and Th determinations 
on the Soviet "Venera-8, -9, and -10," and "Vega-1, and -2" probes (Surkov 
1985) have given us information regarding the chemical nature of the 
surface rock. It is merely important for this paper to note that all of this 
rock belongs to the basalt group and contains almost 10 times more sulfur 
than their terrestrial equivalents. 



It became clear, foUowing the flight by the Soviet "Venera-4" probe 
in 1%7, that CO2 accounts for 97% of the Venusian troposphere, N2 is 
approximately 3%, and the remaining constituents account for approxi- 
mately 0.1% (by volume). Unfortunately, we lack instrumental data on 
chemical composition at elevations below 20 kilometers. This creates con- 
siderable difficulty as we attempt to understand the chemical processes at 
the boundary between the atmosphere and the surface. 

The troposphere of Venus can be seen as a homogenous, weU mixed, 
gaseous envelope for the major constituents (CO2 and N2) and the inert 
gases. It is clear that complex relationships exist between the physical 
(turbulent mixing, and horizontal and vertical planetary circulation of gas 
masses) and chemical (condensation and vaporization of cloud particles, 
gas-phase reactions, and gas-mineral types of interaction) processes in the 
atmosphere which lead to the existence of vertical and horizontal gradients 
of microconstituent concentrations (H2O, SO2 and CO; see Figure 1). 

Venus' high surface temperature can be regarded as a factor which 
enhances the chemical interaction of the atmosphere with surface rock and, 
as a consequence, yields a dependency of the atmosphere's composition on 
heterogenic chemical reactions at the atmosphere-surface boundary. 

Mueller (1964) proposed 25 years ago that three zones may exist in 
the vertical profile of Venus' atmosphere, depending on the predominance 
of varying types of chemical processes: 

• The zone of thermochemical reactions in which the composition of 
the atmosphere is buffered by surface rock minerals; 

• The zone of "frozen" chemical equilibrium, where the composition 
of gases corresponds to their equilibrium ratios in the near-surface layer of 
the troposphere; 

• The zone of photochemical reactions in the upper atmosphere. 

According to this model, chemical reactions at the planet's surface take 
place amid a constant influx of reactive matter from the crust reservoir, as 
geological and tectonic activity also occur. Using the principle of global 
chemical quasiequilibrium in the atmosphere-crust system, we can apply 
thermodynamic computations to estimate the equilibrium concentrations 
of atmospheric gases that are not accessible to direct measurements. 

Lewis (1970) obtained more complete data on calculations of the 
chemical composition of the near-surface atmosphere; he took into account 
the results of the atmospheric analyses performed by the Soviet "Venera-4, 
-5 and -6" probes. Unlike MueUer (1964), he only considered chemical 
equilibrium at the atmosphere-surface boundary (Tible 1). Both of the 



^o^ 10'^ 10' 10 lo-* 10= -> 


FIGURE 1 A schematic vertical cross-section of the troposphere of Venus. It shows 
the distribution of macro- and microconstituents based on data from measurements per- 
formed by the "Venera" series and the "Pioneer Venus" probes. 1: microconstituents; 2: 
macroconstituents; 3: data requiring reSnement. 

above models used the existence of chemical equilibrium throughout the 
troposphere, to its upper cloud boundary. 

The literature has been discussing Urey's (1951) hypothesis for quite 
some time. He proposed "WoUastonite" equilibrium as a mechanism for 
buffering Pcoj in the global, equilibrium atmosphere-crust system (Mueller 
1963; Vinogradov and Volkov 1971; Lewis and Kreimendahl 1980): 

CaCOa + SiOi O CaSiOa + CO2 

calcite quartz Wollastonite 

The thermodynamic calculations performed in these studies demonstrated 
that the mineral association of calcite-quartz-Vollastonite on the surface of 
Venus can buffer Pcoa (~ 90 bar) at a temperature of 742 K. This is virtually 



TABLE 1 C hemical Models of Venus' Troposphere 


of Chemical 


Zone of "Frozen" 




R. Mueller 
1963, 1969 

J. Lewis 1970 

et at. 1976 

el al. 

and Parshev 

Troposphere + Troposphere to an 
lithosphere altitude of 80 km* 

Troposphere + 
surface rock 

Troposphere to lower 
cloud boundary 


Troposphere to an 
altitude of 60 km** 

Spectroscopic measurements 
of CO, Ha. HF, and H,0 

Spectroscopic measurements 
of CO. Ha. HF; H,0 
rVenera-5 & -6" data) 

Chemical analysis of the 
atmosphere on Soviet "Venera 
-4 & -10" probes 

Chemical analysis of the 
atmosphere on Soviet "Venera 
-11 & -12" probes & "Pioneer 

♦Upper boundary of the cloud layer 

••According to Krasnopol'skiy and Parshev (1979): to the "zone of 
photochemical reactions" 

commensurate with the surface conditions. However, interpretation of the 
multisystem computations has shown that carbonates are unstable. Yet, the 
high concentration of SO2 in the troposphere is one of the determining 
factors of this process (Zolotov 1985; Volkov et al. 1986). Consequently, 
"Wollastonite" equilibrium can scarcely be seen as the basis for a chemical 
model of Venus' atmosphere. 

Florenskii et al. (1976) developed the idea in 1976 that there may 
be chemical equilibrium in the subcloud portion of the uoposphere. The 
lower atmosphere was divided into three zones: 

• The stratosphere with an upper layer of clouds, which is the zone 
of photochemical processes; 

• The main cloud layer zone, where photochemical (above) and 
thermochemical (below) processes compete; 

• The portion of the troposphere below the cloud base, which is the 
zone where thermochemical equilibria are predominant. 

This model brought us to a closer understanding of the Venuslan 
troposphere as a complex, predominantly nonequilibrlous system, even 
though numerical estimates of microconstituent concentrations (primarily 
SO2) departed greatly from the actual values (Tkble 2). 


TABLE 2 Chemical Composilion of the Venusian Near-Surface Troposphere from 
CompuUtional Data (Rehtive Levels of Microconstituents by Volume). 




















2- 10-' 












5.2- 10 » 

310 ' 











210 • 









2.410 » 





81 a" 





1.8- 10-' 

Notes: The underlined figures are initial data of measurements on space probes or ground- 
based fadlilies; 1: MueUer (1969); 2: Lewis (1970); 3: Khodakovskiy er al. (1979); 4: 
Krasnopol'skiy and Parshev (1979); 5: Zolotov (1985). 

Column 6 Ubulates daU of measurements made on the "Venera" and Tioneer Venus" probe 
series; no measurements were performed below an altitude of 20 kilometers (Kgure 1). 

Following measurements of the chemical composition of the tropo- 
sphere by the Soviet "Venera-11 and -12" probes and the "Pioneer Venus" 
probe, the computational and experimental values of microconstituent con- 
centrations were compared. Khodakovskii et al. (1979) and Krasnopol'skii 
and Parshev (1979) concurrently and independently proposed models (Tk- 
ble 2). These models were the first to compare gas-phase reaction rates 
with troposphere mixing rates. These consequences were generated: 

• The troposphere is generally in nonequilibrium, with the exception 
of the near-surface layer with a thickness of the first kilometer, where 
the highest temperatures are dominant. However, the processes of het- 
erogeneous catalysis at the atmosphere-surface boundary may favor the 
establishment of chemical equilibrium in relation to certain constituents; 

• The chemical composition of the microconstituents in the vertical 
cross-section below the cloud base region of the troposphere does not 
vary: it corresponds to the "frozen" equilibrium at the atmosphere-surface 
boundary (T = 735 K; P = 90 atm). 

The principal of "frozen" equilibrium was applied in order to theoret- 
ically estimate the chemical composition of cloud particles; this enables us 
to better understand the sulfur and chlorine cycles in the atmosphere-crust 
system (Volkov 1983; Volkov et al. 1986). 

The lack of instrumental determinations of microconstituents in the 


troposphere at altitudes below 20 kilometers prevents us from solving the 
critical problem of the ratio of gaseous sulfur: HjS + COS > SO2 (Lewis 
1970) or H2S + COS < SO2 (Khodakovskii et al. 1979; see Tkble 2). 
Furthermore, gas chromatographic determination of oxygen by the Soviet 
"Venera-13, and -14" probes cannot be reconciled with the concurrent pres- 
ence in these same samples of 80 ppm H2S and 40 ppm COS (see Volkov 
and Khodakovskii 1984 for greater detail). The only original attempt to 
experimentaUy estimate the oxidation-reduction regime on Venus' surface, 
using a "Kontrast" detector on the Soviet "Venera-13, and -14" probes 
(Florenskii et al. 1983) pointed to the presence in the near-surface layer of 
the troposphere of a reducing agent (CO). However, it does not give us a 
clear-cut solution to the oxygen problem. 

The results from estimations of the chemical composition of the tro- 
posphere and the nature of the processes occurring in its near-surface layer 
can be summarized in three conclusions: 

(1) Chemical equilibrium in the troposphere of Venus has generally 
not been reached. 

(2) The vertical gradients of SO2, H2O and CO concentrations are 
a function of the competition between physical and chemical processes in 
the troposphere. 

(3) The near-surface troposphere can be seen as a layer in a state of 
"frozen" chemical equilibrium. 

Unfortunately, we have yet to resolve the question of the oxidation- 
reduction regime on Venus' surface, as well as the problem of the existence 
of free oxygen in the troposphere. 


Many investigations have attempted to estimate the possible mineral 
associations on the surface of Venus using chemical thermodynamic meth- 

Mueller published the first such study as a component of the afore- 
mentioned chemical model of the atmosphere (Mueller 1963) and obtained 
the following results: 

• Tfemperature and pressure on Venus' surface are consistent with 
silicate-carbonate equilibrium, and carbon is bound in the rock in CaCOa 


• Oxygen partial pressure is buflered by Fe-containing minerals; 

• Graphite and the native metals are not stable; 

• Nitrogen is not bound in the condensed phases; 


• A number of chlorine- and fluorine-containing minerals are stable 
at the surface. 

Lewis (1970) calculated 64 mineral equilibria in order to estimate P 
and T on the surface before the probes performed these measurements. 
One out of three proposed options for the P and T values was in satisfactory 
agreement with the actual values obtained a year later. Lewis yielded the 
following, additional forecast estimates: 

• Surface rock contains H2O molecules bound in the form of tremo- 

• sulfur is bound in the cloud layer in the form of mercury sulfides. 
Carbonyle-sulfide is the dominant form in which sulfur is found in the 
troposphere. This prediction proved only partially true: sulfur is actually 
the main component of cloud particles, but the latter consist primarily of 

A series of studies to calculate mineral composition was conducted in 
1979-83 at the VI. Vernadskiy Institute using the computation of the phase 
ratios in multicomponent, gaseous systems, modeling the atmosphere/sur- 
face-rock system. The computations were based on troposphere chemical 
analysis data from the Soviet "Venera" series of probes, "Pioneer Venus," 
thermodynamic constants of about 150 phases, the chemical components 
of terrestrial magmatic rock, and the results of x-ray-fluorescent analysis of 
rock at three probe landing sites ("Venera-13," "Venera-14," and "Vega- 
2"). Compilation of this material can be found in Volkov et al. (1986). It 
should be stressed that three important predictive conclusions were made 
before the first data on the chemical composition of Venus' bedrock were 

• Sulfur may be bound as sulfates (CaSO^) and/or sulfides (FCS2), 
and its concentration greatly exceeds known sulfur levels in terrestrial 

• Water-containing minerals are unstable; 

• Carbonates are unstable; 

• Magnetite Fe304 must be a widespread constituent both as primary 
and as altered bedrock. 

These conclusions were generally confirmed, albeit with some refine- 
ment, by comparing them with X-ray-fluorescent analyses at "Venera-13," 
"Venera-14" and "Vega-2" landing sites, and by further, more detailed 
theoretical investigations (Zolotov 1985, 1989). 

Sulfur at the surface probe landing sites, if we judge from the data 
of additional, postflight calibration investigations (Surkov et al. 1985), is 
in an anhydrite form (CaS04). Sulfur content may serve as a measure of 
convergence to the state of chemical equilibrium relative to SO2 in the 


atmosphere-crust system (Lewis and Prinn 1984; Volkov et al. 1986). It 
may be possible that rock with a maximum level of sulfur (1.9 mas. %, 
"Vega-2") were in contact with the atmcKphere longer than the bedrock at 
the landing sites of the Soviet "Venera-13" and "Venera-14" probes. 

In his 1985 study, Zolotov conducted thermodynamic assessments of 
carbonate stability depending on the concentration of SO2, since a reaction 
such as: 

CaCOs + I.55O2 <^ CaSOi + CO2 + 0.2552 

takes place in Venus surface conditions free of kinetic constraints. As it 
turned out, the presence of SO2 in quantities exceeding 1 ppm excludes 
the existence of calcite and dolomite. However, magnesite (MgCOs), as a 
product of the alteration of pure forsterite, MgSi04 (Foioo), may be stable 
at altitudes of 1.5 to eight kilometers. 

Zolotov demonstrated in this same study (1985) that hematite (Fe203) 
may even be stable at an altitude of more than 1.5 kilometers (Figure 2), in 
addition to magnetite (Fe304) (the product of water vapor-driven oxidation 
of Fe-containing siUcates, CO2 and SO2). Hematite stability is apparently 
confirmed by the results obtained from interpreting the surface color on 
the TV images from "Venera-13 and -14" (Shkuratov et al. 1987). 

Nevertheless, in their 1980 study Lewis and Kreimendahl retain the 
conclusion regarding calcite (CaCOa) and wiistite (FeO) stability, while 
allowing for the prevalence of H2S and COS over SO2 in condiUons of 
total chemical equilibrium at the surface-atmosphere boundary. They come 
to the same logical conclusion that in this case, the surface rock of Venus' 
crust is characterized by an extremely low degree of oxidation (Fe-|-3/Fe+2 
at one to two orders lower than the terrestrial value). Strictly speaking, the 
ultimate solution to the problem of the oxidation of Venus' crust has not 
been found due to the lack of instrumental data. 

In 1975, Walker (1975) drew attention to the possible dependence of 
the mineral constituents of Venus' surface on the hypsometric level. The 
pressure (« 65 atm.) and temperature (w 100 K) gradients are actuaUy 
so great that they may alter the composition of the phases of rock during 
their exogenous cycle, that is, under the influence of aeolian transport. If 
we take into account the fact that our knowledge of Venus' mineralogy 
does not go beyond the framework of theoretical forecasting, the factor of 
"hypsometric control" must still be considered hypothetical. 

Let us summarize the theoretical investigations of the chemical inter- 
action of Venus' rock with its atmosphere. 

• Alteration of the composition of Venus' basalts during interaction 
with the atmosphere is highly probable; 


FIGURE 2 Estimates of the oxidation-reduction regime in the troposphere and on the 
surface of Venus from data produced by measurements (1,2,5) and computations (3,4). 
(Zolotov 1985). 1. CO2 = CO + i02 (CcO:, = 96.5%; Ceo = 20 ppm). Z SO2 = 
|S2 + O2 (C502 = 130 -=- 185 ppm; C52 = 20 ppb). 3. 3Fe203 = 2Fe304 + ^03 
(buffer HM). 4. 2Fe304+ 3Si02 = 3Fe2Si04 + O2. 5. "Kontrast" detector (Flottnskiy 
el a!. 1983). 

• Apparently, the primary outcome stemming from this interaction 
will be the sink of sulfur in the crust as anhydrite (CaS04) and/or iron 
sulfides (FeS and FeS2); 

• The existence of carbonates (besides MgCOa), free carbon and 
nitrogen compounds on the surface of Venus is thermodynamically prohib- 

• The lack of complete factual data prevents our making a clear-cut 
conclusion as to the stability of water-bearing minerals and the degree of 
oxidation of the Venusian crust. 


Interpretation of data on Venus' atmospheric chemistry, and in par- 
ticular, consideration of the photochemical processes in the stratosphere 
(Krasnopolskii 1982; Yung and De More 1982) demonstrated that nitrogen 
and carbon cycles are completed in the atmosphere. The H2O cycle poses 
more problems, since we are not yet clear on the vertical profile of H2O 
concentrations in the near-surface atmosphere. 

Clearly, sulfur is the only volatile element on Venus which, in the 



h, KM 
80 H 


^i . 




[CO J.^^;C0] +01^ ^^y^^^' 






1 .._2 3 4 —5 

FIGURE 3 Diagram of the cycles of CO2, sulfur and chlorine in the Venusian atmosphere 
1: chlorine cycle; 2: CO2 cycle; 3: rapid sulfur cycle; 4: slow sulfur cycle; 5: sulfur flux 
into the crust. 

contemporaiy geological epoch, participates in the cyclical mass exchange 
between the atmosphere and the crust. Sulfur's behavior as a constituent 
of the cloud layer essentially determines its structure and dynamics. Three 
cycles (Figure 3) have been discerned, depending on the rates at which 
these processes unfold (Lewis and Prinn 1984). 

The rapid cycle takes place in the stratosphere and the clouds and 
sets the stage for the photochemical emergence and thermal destruction of 
sulfuric acid aerosols. The residence time for the SO2 molecule is estimated 



TABI^ 3 MinertI Composilioi of Veniuin Surfioc Rock Based on Theofelical Assessmenu 

(Secondary Mineral 




Carbon in CaCO, 
C(,^j., i. 

Carbonates Ca and Mg 

Carbonates are unsuble 
MgCO, (?) 

H^ in imphiboles 
and micas 

HjO in ampbiboles 

Amphiboles (7) 

Fe,0,. Fe,0, 

FeO, Fe,0< where 

''cos ■•■ ^H2S * ^^502 

FejO^, Fe^Oj (7) where 
'^os ■•■ ''his '^ "502 

Sulfur in sulfides of Fe and 

anhydrite (CaSO^) 

PredominanUy CaSO,, 
sulfides of Fe are suble 

Nitrogen-bearing minerals arc unstable 

Chlorine- and fluoride-bearing minerals are suble (fluorite/apatite?) 

1. Mueller 1963, 1969 

2. Lewis 1970; Lewis and Kreimendahl 1980 

3. Khodakovskiy el at. I97S: Volkov 1983; Zolotov 1989. 

to be from several hours to several years. TVo alternative scenarios are 
proposed in T^ble 4. It is difficult to select between the two because of the 
lack of experimental data on the rates of certain photochemical reactions. 

The slow atmospheric cycle is most likely a function of photochemical 
and thermodynamic reactions in the lower atmosphere which lead to the 
existence of reduced forms: H2S and COS and elementary sulfur. Ap- 
parently, the stratosphere is the region of H2S and COS flux: they either 
photodissociate there or are oxidized by molecular oxygen to SO3. The 
time span of sulfur molecules in the cycle is estimated to be several dozen 
years (Lewis and Prinn 1984). 

The mass exchange between Venus' crust and its atmosphere is carried 
out in a "geological" sulfur cycle. The source of sulfur is crust matter which 
produces sulfur-bearing gases through both volcanism and the interaction 
of minerals with atmospheric gases, such as FeS2 with CO2, H2O, and CO. 

These gases repeatedly participate in photo- and thermodynamic pro- 
cesses in the atmosphere. The rapid atmospheric cycle brings about the 
long-term existence of a cloud cover made up of condensed H2SO4 parti- 
cles. The competition of photo- and thermochemical reactions in the slow 
cycle apparently support the existence of SO2 as the dominant form of 
sulfur in the atmosphere. An excess of SO2 compared with its equilibrium 
concentration in the atmosphere-crust system create an SO2 flux in the 
form of sulfates in surface rock. 

TWo factors determine the scales and rates of flux: 


TABLE 4 Sulfur Cycles on Venm 


Timeframe I. Fast cycle (stratosphere and cloud layer) 

(Winick and Stewart 1980) (Knisnopol'skiy 1982) 

COj + hv -» CO + O SOj + hv ^ SO + O 

< 10 yrs. SO2 + O + M ^ SOj + M SO + O + M -» SOj + M 

(OH. HO2 arc calalysers) SO, + O + M -» SOj + M 

SOj + HjO ^ HjSO^ (Sol) SO3 + HjO -^ H2S04(SoI) 

n. Slow cycle (lower atmosphere and cloud layer) 
SOj + 4CO -> COS + 3S0j SO3 + Hj + 3CO -♦ HjS + SCO, 
> 10 yrs. COS + hv ^ CO + S HjS + hv -> HS + H 

COS + 1.50j ^ SOj + CO H2S + 1.50j -> SO3 + Hj 

in. Geological Cycle 
CaSiOj, CaAliSiiO, + SOj -» CaSO^ 
> 10* yrs. FeSiOj. Fe^ -^ COS (H^S) -» FeS(FeS,) 

The time frame for a cycle to ran its course depends on: 

1) Mineral ti gas reaction rates on the pUnet'i surface 

2) Length of time during which mineral particles are in coiuct with the almogphere 
such as surface relief renewal rales 

• The rate of heterogeneous mineral = gas reactions on the planet's 


• The residence span in which mineral particle are in contact with 
the atmosphere, for example, the surface relief renewal rate. 

The completing of the "geological" cycle probably occurs as the altered 
surface rock (rich CaS04) is re-melted in the deep regions of the crust. 
Attenuated volcanic and tectonic activity on Venus ultimately reduces the 
thickness of the cloud layer because sulfur is fixed in the crust and depleted 
in the atmospheric reservoir. 


We can cite at least four firmly established facts that determine the 
existence of the chemical interaction of Venus' atmosphere with its surface 
rock- These are: 


• Loosely porous rock on the planet's surface is developed; massive 
rock display traces of corrosion and degradation; 

• There is no global regolith; aeolian transport on a limited scale is 
supported by weak winds in the near-surface atmosphere; 

• The troposphere contains reactive gases (microconstituents): SO2, 
H2O, CO, and others;- Venus' basalts contain one to 1.5 more orders of 
sulfur than their terrestrial equivalents. 

We can make the following conclusions based on our interpretation of 
the entire set of observational data: 

(1) The processes of lithospheric-atmospheric interaction substantially 
alter primary basalts and subject them to chemical weathering. The scale 
of this process cannot be estimated; 

(2) The troposphere is generally not in a state of chemical equilibrium 
with the surface rock, and the chemical composition of the near-surface 
layer may correspond to a "frozen" equilibrium which is buffered by the 

(3) Sulfur is in a state of cyclical mass exchange between the atmo- 
sphere and the crust. 

(4) Nitrogen and oxygen in the crust's rock do not form stable phases. 
Their cycles become completed in the atmosphere. 


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Runaway Greenhouse Atmospheres: 
Applications to Earth and Venus 

James F. Kasting 
The Pennsylvania State University 


Runaway greenhouse atmospheres are discussed from a theoretical 
standpoint and with respect to various practical situations in which they 
might occur. The critical solar flux required to trigger a runaway greenhouse 
is at least 1.4 times the solar flux at Earth's orbit (So). Rapid water loss 
may occur, however, at as little as 1.1 S,,, from a type of atmosphere 
termed a "moist greenhouse." The moist greenhouse model provides the 
best explanation for loss of water from Venus, if Venus did indeed start 
out with a large amount of water. The present enrichment in the D/H 
ratio on Venus provides no unambiguous answer as to whether or not 
it did. A runaway greenhouse (or "steam") atmosphere may have been 
present on the Earth during much of the accretion process. Evidence from 
neon isotopes supports this hypothesis and provides some indication for 
how long a steam atmosphere may have lasted. Finally, the theory of 
runaway and moist greenhouse atmospheres can be used to estimate the 
position of the inner edge of the continuously habitable zone around the 
Sun. Current models place this limit at about 0.95 AU, in agreement with 
earUer predictions. 


The topic of runaway greenhouse atmospheres has received renewed 
attention over the past several years for three different reasons. The first 
concerns the history of water on Venus. Although there is still no concensus 
as to whether Venus had much water to begin with (Grinspoon 1987; 




Grinspoon and Lewis 1988), some recent theories of accretion (Wetherill 
1985) predict extensive radial mixing of planetesimals within the inner solar 
system. If this idea is correct, then Venus must initially have received a 
substantial fraction of Earth's water endowment. This water is obviously 
not present on Venus today. The mixing ratio of water vapor in the lower 
atmosphere of Venus is approximately 10"''; thus, the total amount of 
water present is only about lO"^ times the amount in Earth's oceans. The 
runaway greenhouse theory provides a convenient explanation for how the 
rest of Venus' water might have been lost. 

A runaway greenhouse atmosphere may also have been present on 
Earth during at least part of the accretionary period. Matsui and Abe 
(1986a,b) and Zahnle et al. (1988) have shown that an impact-induced 
steam atmosphere could have raised the Earth's surface temperature to 
1500 K, near the solidus temperature for typical silicate rocks. This implies 
the existence of a global magma ocean of unspecified depth. Although 
the continuous existence of such a steam atmosphere has been questioned 
(Stevenson 1987), an analysis of terrestrial neon isotope data (Kasting 1990) 
strongly supports the notion that such an atmosphere existed during some 
portion of the accretionary period. 

A third reason for interest in runaway greenhouse atmospheres con- 
cerns their implications for the existence of habitable planets around other 
stars. Any planet that loses its water as a consequence of a runaway green- 
house effect is not likely to be able to support life as we know it. Thus, 
the idea that runaway greenhouses are possible sets limits on the width of 
the continuously habitable zone (CHZ) around our Sun and around other 
main sequence stars (Hart 1978, 1979; Kasting and Tbon 1989). One of 
the most important reasons for studying runaway greenhouses is to try to 
estimate the chances of finding another Earth-like planet elsewhere in our 

Here, the theory of runaway greenhouse atmospheres is briefly re- 
viewed, and the consequences for the three problems mentioned above are 


The concept of the runaway greenhouse atmosphere was introduced 
by Hoyle (1955) and has been further developed by Sagan (1960), Gold 
(1964), Dayhott etal. (1%7), IngersoU (1969), Rasool and DeBergh (1970), 
Pollack (1971), Goody and VN^lker (1972), Walker (1975), V^tson et al. 
(1984), Matsui and Abe (1986a,b), Kasting (1988), and Abe and Matsui 
(1988). The basic idea, as explained by IngersoU (1%9), is that there exists 
a critical value of the solar flux incident at the top of a planet's atmosphere 
above which liquid water cannot exist at the planet's surface. Intuitively, 


one expects this to be the case. If Earth were by some means to be pushed 
closer and closer to the Sun, one would anticipate that at some point the 
oceans would be vaporized and the planet would be enveloped in a dense, 
steam atmosphere. The amount of water in Earth's oceans, 1.4 x lO^"* g, is 
such that the surface pressure of this atmosphere would be about 270 bar. 
For comparison, this is ~50 bar greater than the pressure at the critical 
point of water (647.1 K, 220.6 bar). 

It should be noted that the term "runaway greenhouse" has also been 
used to describe the positive feedback between the surface temperature of 
a planet and the amount of water vapor in its atmosphere. An increase in 
surface temperature causes an increase in the vapor pressure of water which, 
in turn, leads to an enhanced greenhouse effect and a further increase in 
surface temperature. Although this type of positive feedback certainly 
exists, there is no reason to believe that Earth's present climate system is 
unstable. Surface temperature is simply a monotonically increasing function 
of the incident solar flux. Thus, the phrase "runaway greenhouse" is best 
reserved to describe a situation in which a planet's surface is entirely devoid 
of liquid water. 

The single most important characteristic of a runaway greenhouse at- 
mosphere is the critical solar flux required to trigger it. Only recently have 
detailed estimates of this energy threshold been made (Kasting 1988; Abe 
and Matsui 1988). Even these estimates, which were obtained using elab- 
orate radiative-convective climate models, cannot be considered reliable. 
The greatest uncertainty in performing such a calculation is the effect of 
clouds on the planetary radiation budget. Kasting (1988) has derived results 
for a fully saturated, cloud-free atmosphere. (Actually, clouds were crudely 
parameterized in this model by assuming an enhanced surface albedo.) 
The critical solar flux in his model is 1.4 S,,, where S„ is the present solar 
flux at Earth's orbit (1360 W m-^). An Earth-like planet with Earth-like 
oceans was assumed. Abe and Matsui (1988) have performed a similar 
calculation for a case in which part of the energy required to trigger the 
runaway greenhouse was derived from infalling planetesimals. (Their study 
vms specifically directed at the problem of atmospheric evolution during the 
accretion period.) The amount of accretionary heating required to trigger 
runaway conditions in their model, 150 W m~^, is the same as the value 
derived by Kasting (1988) for an analogous simulation. (See his Figure 13.) 
Thus, the two existing detailed calculations of the energy threshold of the 
runaway greenhouse are in good agreement 

Although clouds cannot reliably be parameterized in such an atmo- 
sphere, their qualitative effect on the planetary radiation balance is not 
diflicult to determine (Kasting 1988). An atmosphere rich in water vapor 
would probably exhibit at least as much fractional cloud cover as the current 



Earth and possibly much more. Although clouds affect both the incom- 
ing solar and outgoing infrared radiation, the solar effect should dominate 
because a water vapor atmosphere would already be optically thick through- 
out the infrared. Thus, the main effect of increased cloud cover should 
be to reflect a greater proportion of the incident solar radiation, thereby 
diminishing the amount of energy available to sustain a steam atmosphere. 
It follows that the energy threshold for a runaway greenhouse is almost 
certainly higher than 1.4 S^. How much higher is uncertain, but values as 
high as 5 S,, are within the reahn of possibility (Kasting 1988, Figure 8c). 

These rather speculative theoretical models should be weighed against 
an observational fact: our neighboring planet Venus has very little water in 
its atmosphere, less than 200 ppm by volume (Moroz 1983; von Zahn et al. 
1983). As discussed further below, it is not clear whether this lack of water 
is innate to the planet or whether it is the result of an evolutionary process. 
One possibility, however, is that Venus was initially water-rich, and that 
it lost its water by photodissociation in the upper atmosphere followed by 
escape of hydrogen. (See references in opening paragraph.) If this theoiy 
is correct, then Venus must have experienced either a runaway greenhouse 
or a phenomenon akin to a runaway greenhouse at some time in the past. 
The solar flux at Venus' orbit is currently 1.91 So. Based on steUar evolution 
models, the Sun's output was some 25-30% lower (1.34-1.43 S<,) early in 
solar system history (Gough 1981). This implies that the critical threshold 
for losing water from a planet is no higher than 1.9 S„ and may well be 
considerably lower. 

If this was all there was to the problem, one could reliably conclude 
that the energy threshold for the runaway greenhouse was between 1.4 S,, 
and 1.9 S,,. However, it has recently been demonstrated that there are other 
ways for a planet to lose water rapidly besides the runaway greenhouse. An 
alternative possibility, proposed by Kasting et al. (1984) and Kasting (1988) 
is that Venus experienced a so-called "moist greenhouse," in which the 
planet lost its water while at the same time maintaining liquid oceans at its 
surface. This turns out to be slightly favored from a theoretical standpoint; 
it also requires a significantly lower energy input than does the runaway 
greenhouse model. This alternative theory is described briefly below. 


The concept of the moist greenhouse atmosphere stems from the 
analysis of moist adiabats by IngersoU (1%9). IngersoU showed that the 
vertical distribution of water vapor in an atmosphere should be strongly 
correlated with its mass-mixing ratio c<,(H20) near the surface. When water 
vapor is a minor constituent of the lower atmosphere [c<,(H20) < 0.1], 
its concentration declines rapidly with altitude throughout the convective 


region as a consequence of condensation and rainouL This is the situation 
in Earth's atmosphere today, where C<,(H20) declines from roughly 0.01 
near the surface to about 3 x 10~® in the lower stratosphere. When water 
vapor is a major constituent [Co(H20) > 0.1], however, its behavior is quite 
different. The amount of latent heat released by condensation becomes 
so large that the temperature decreases very slowly with altitude, and the 
water vapor mixing ratio remains nearly constant. This allows water vapor 
to remain a major constituent even at high altitudes which, in turn, allows 
it to be effectively photodissociated and the hydrogen lost to space. (The 
important constraint here is that water vapor remain abundant above the 
cold trap, i.e. the maximum height at which it can condense. When this 
criterion is satisfied, hydrogen should escape at clcse to the diffusion-limited 
rate (Hunten 1973), as long as sufficient solar extreme ultraviolet (EUV) 
energy is available to power the escape.) 

Kasting et al. (1984) and Kasting (1988) have applied the moist green- 
house model to the problem of water loss from an Earth-like planet The 
most recent results (Kasting 1988) indicate that hydrogen escape becomes 
very rapid (i.e. Co(H20) becomes greater than 0.1) for incident solar fluxes 
exceeding 1.1 So. As before, this calculation was performed for a fulfy 
saturated, cloud-free atmosphere, so the actual value of the solar flux at 
which water loss becomes efficient is probably greater than this value. The 
calculation does demonstrate, however, that Venus could have lost most of 
its water without ever experiencing a true runaway greenhouse. Indeed, 
the solar flux at Venus's orbit early in solar system history (1.34 - 1.43 
So) is so close to the minimum value required for runaway (1.4 So) that 
it seems likely that clouds would have tipped the balance in favor of the 
moist greenhouse scenario. Thus, if Venus were originally endowed with as 
much water as Earth, it may at one time have had oceans at its surface. 

With the concepts of runaway and moist greenhouses in mind, let us 
now return to the three topics mentioned in the introduction. 


The real issue concerning Venus is not so much whether it could have 
lost its water but, rather, whether it had any appreciable amount of water 
initially. It is now well accepted that the D/H ratio on Venus is very high: 
approximately 100 times the terrestrial value. The original interpretation 
of this observation (Donahue et al. 1982) was that Venus was once wet. 
If Venus and Earth started out with similar D/H ratios, which seems even 
more likely now in view of the terrestrial D/H ratio observed in the tail 
of comet Halley (Eberhardt et al. 1987), this measurement implies that 
Venus once had at least 100 times as much water as it does now. The 
current water abundance on Venus, assuming a lower atmosphere mixing 


ratio of 100 ppmv, is only 0.0014% of a terrestrial ocean. Thus, this 
minimal interpretation requires only that Venus start out with about 0.1% 
of Earth's water endowment Even advocates of a dry early Venus would 
probably not dispute such a claim, given the potential for radial mixing of 
planetesimals during the accretion process (Wetherill 1985). If, however, 
some deuterium was lost along with the escaping hydrogen (which seems, 
indeed, to be unavoidable), the amount of water that was lost could be 
orders of magnitude greater. Consequently, proponents of a wet origin for 
Venus (Donahue et al. 1982; Kasting and Pollack 1983) have suggested that 
Venus may well have started out with an Earth-like water endowment. 

The wet- Venus model has been challenged by Grinspoon (1987) and 
Grinspoon and Lewis (1988), who point out that the present D/H en- 
richment on Venus could be explained if the water abundance in Venus' 
atmosphere were in steady state. Loss of water by photodissociation and 
hydrogen escape could be balanced by a continued influx of water from 
comets. Grinspoon and Lewis's steady-state model has, in turn, been crit- 
icized (Donahue, private communication, 1988) on the grounds that they 
underestimated the amount of water vapor in Venus' lower atmosphere. 
The time constant for evolution of the DfH ratio in Venus' atmosphere can 
be expressed as (Grinspoon 1987) 

T ~ R/{f<i>) (1) 

where R is the vertical column abundance of water vapor in the atmosphere, 
<j> is the hydrogen escape rate, and f is the D/H fractionation factor (i.e. 
the relative efficiency of D escape compared to H escape). Best estimates 
for the values of <l> and f, based on a weighted average of the hydrogen 
loss rates from charge exchange with H+ and from momentum transfer 
with hot O atoms, are 2 x 10^ H atoms cm"^ s'^ and 0.013, respectively 
(Hunten et al. 1989). This estimate draws upon a reanalysis of the charge 
exchange process by Krasnopolsky (1985). Grinspoon (1987) assumed that 
the Venus lower atmosphere contained only 20 ppmv of water vapor; this 
gives R « 6 X 10^^ H atoms cm"' and r « 7 x 10^ years. Even this 
value is somewhat longer than the age of the solar system, indicating that 
the steady-state model is marginally capable of explaining the observations. 
Small increases in the value of either .^ or f could eliminate the time scale 
problem. If the H2O mixing ratio is actually closer to 200 ppm, however, 
then r Rs 7 X 10^° years, and the steady-state model is in serious trouble. 
Resolution of this question requires, at a bare minimum, that the 
present controversy regarding the H2O content of the Venus lower atmo- 
sphere be resolved. Our present understanding of Venus' water inventoiy 
is further muddled by the fact that the H2O mixing ratio apparently varies 
with altitude from about 20 ppmv near the surface to 200 ppmv just below 


the clouds (von Zahn et al. 1983). Until this variation is explained theoret- 
ically, little confidence can be given to any of the measurements, and the 
H2O abundance on Venus will remain an enigma. 

Setting aside the problem of the initial water endowment, subsequent 
aspects of the evolution of Venus' atmosphere are now reasonably well 
understood (Kasting and Tbon, 1989). If Venus had water originally, most 
of it was lost through either the runaway or moist greenhouse processes 
described above. One additional reason for favoring the moist greenhouse 
model is that it might have facilitated removal of the last few bars of 
Venus' water (Kasting et al, 1984). If an ocean had been present on 
Venus for any significant length of time, it should have drawn down the 
atmospheric CO2 partial pressure by providing a medium for the formation 
of carbonate minerals. A thinner atmosphere would, in turn, have provided 
less of a barrier to loss of water by photodissociation followed by hydrogen 
escape. For example, suppose that an initial 100-bar CO2-N2 atmosphere 
was reduced to 10 bar of total pressure by carbonate formation. The critical 
water abundance at which the cold trap became effective would then be 
reduced from 10 bar to 1 bar, based on the criterion Co(H20) < 0.1. Only 
1 bar of water would then need to be lost by the relatively inefficient 
hydrogen loss processes that would have operated after the cold trap had 

Once surface water was depleted, carbonate formation would have 
slowed dramatically, and CO2 released from volcanos should have begun 
accumulating in the atmosphere. SO2 concentrations would have likewise 
increased, and the modem sulfuric acid clouds would have started to 
form. Thus, regardless of its initial condition, Venus' atmosphere should 
eventually have approached its modern state. 


The possibility that Earth was enveloped in a dense steam atmosphere 
during the accretionaiy period was raised by Matsui and Abe (1986a,b, 
and earlier references therein). Their model elaborated on earlier studies 
(Benlow and Meadows 1977; Lange and Ahrens 1982) that predicted 
that infalling planetesimals would be devolatilized on impact once the 
growing Earth had reached about 30% of its present radius. The water 
contained in these impactors would thus ha\% been emplaced directly 
into the protoatmosphere, instead of following the more traditional route 
of being first incorporated into the solid planet and being subsequently 
outgassed from volcanos. 

A critical aspect of Matsui and Abe's model was that it considered the 
effect of the impact-induced steam atmosphere on the planetary radiation 
budget. Based on a relatively crude, grey-atmosphere, radiative-equilibrium 


calculation, they argued that the surface temperature of such an atmosphere 
would rise to the approximate solidus temperature of crustal rocks, about 
1500 K The surface pressure would continue to rise until it was of the order 
of 100 bar. At this point dissolution of water in the partially molten plane- 
tary surface would balance the continued input of water from planetesimals 
and thereby stabilize the atmospheric pressure and temperature. 

Matsui and Abe's fundamental predictions have been largely borne out 
by studies carried out using more detailed models (Kasting 1988; Zahnle 
et al. 1988; Abe and Matsui 1988). Given an accretionary time scale of 
10^ to 10^ years (Safronov 1969), the rate of energy release from infaUing 
material should indeed have been sufficient to maintain the atmosphere in 
a runaway greenhouse state (Kasting 1988, Figure 13). One objection that 
has been raised, however, is that none of these models have taken into 
account the stochastic nature of the accretion process (Stevenson 1987). 
If the latter stages of accretion were dominated by large impacts spaced 
at relatively long time intervals (Wetherill 1985), a steam atmosphere may 
have existed only for short time periods following these events. 

Some light can be shed on this otherwise difficult question by an 
analysis of neon isotopic data. Craig and Lupton (1976) pointed out some 
time ago that the ^''Ne/^^Ne ratio in Earth's atmosphere (9.8) is lower 
than that in gases thought to originate in the mantle. Their database 
has now been expanded to include volcanic gases, along with trapped 
gases in diamonds and MORBs (mid-ocean ridge basalts) (Ozima and 
Igarashi 1989). The neon isotope ratio in gases derived from the mantle 
is generally between 11 and 14, with the lower values attributed to mixing 
with atmospheric neon (Ozima and Igarashi 1989). Thus, the ^^Ne/^^Ne 
ratio of mantle neon is similar to the solar ratio, which ranges from 13.7 in 
the solar wind to 11-12 in solar flares (Ozima and Igarashi 1989). 

The neon isotopic data are most easily explained if Earth formed 
from material with an initially solar 2°Ne/^^Ne ratio, and if ^°Ne was 
preferentially lost from Earth's atmosphere during rapid, hydrodynamic 
escape of hydrogen (Kasting 1990). The requirements for losing neon 
are quite specific and can be used to set rather tight constraints on the 
composition of Earth's atmosphere at the time when the escape occurred. 
The minimum hydrogen escape flux required to carry off ^°Ne is 2 x 
10^^ H2 mol cm~2 s-i (Kasting 1989). If the background atmosphere at 
high altitudes was predominantly CO2, the diffusion-limited escape rate of 
hydrogen is given by 

<j>um « 3 X 10" f{H2)l{\ -I- f{H2)]cm-^s-' (2) 

where f(H2) is the atmospheric H2 mixing ratio (Hunten 1973). By com- 
paring this expression with the escape rate needed to carry off neon, one 


can see that this is only possible if f(H2) exceeds unity, i.e. the atmosphere 
must be composed primarily of hydrogen. Such an atmospheric composi- 
tion would have been very difficult to sustain during most of Earth's history. 
However, it is entirely reasonable in an impact-induced steam atmosphere, 
where copious amounts of H2 could have been generated from the reaction 
of H2O with metallic iron. 

A second reason that the escape of neon mtist have occurred early is 
that this is the most favorable period from an energetic standpoint The 
solar EUV energy flux required to power an escape rate of 2 x 10*^ H2 
mol cm~^ s~' is about 40 ergs cm~^ s~^ or roughly 130 times greater 
than the present solar minimum EUV flux (Kasting 1989). EUV fluxes of 
this magnitude are expected only within the first 10 million years of solar 
system history (Zahnle and ^^Iker 1982). Thus, the isotopic fractionation 
of neon must have taken place during the accretionary period, most likely 
in a steam atmosphere of impact-induced origin. 

If this explanation for the origin of the atmospheric ^°Ne/^^Ne ratio 
is correct, it is possible to use this information to estimate the length of 
time that a steam atmosphere must have been present on the growing 
Earth. According to theory (Zahnle et al. 1988), the surface pressure of the 
steam atmosphere should have been buffered at a more or less constant 
value of ~ 30 bar. Application of the "constant inventory" model for 
hydrodynamic mass fractionation (Hunten et al. 1987) then predicts that 
the escape episode must have lasted at least five million years (Kasting 
1989). TTius, even if large impacts were important and steam atmospheres 
were essentially a transient phenomenon, the neon isotope data implies 
that such conditions may have obtained during an appreciable fraction of 
the accretionary period. 

An alternative theory for explaining the isotopic abundance pattern of 
atmospheric neon (and xenon) is that the fractionation occurred during the 
loss of a primordial H2 atmosphere captured from the solar nebula (Sasaki 
and Nakazawa 1988; Pepin, manuscript in preparation). This theory appears 
equally viable in terms of its ability to explain the isotopic data. It differs 
from the steam atmosphere model in that it requires that the accretion 
process proceed in the presence of nebular gas. If the lifetime of the solar 
nebula was much less than the accretionary time scale, as predicted by 
Safronov (1%9), then the steam atmosphere model is preferred. 


A third reason that runaway (and moist) greenhouse atmospheres are 
of interest is that they set constraints on the inner edge of the continuously 
habitable zone (CHZ) around the Sun (Kasting et al. 1988; Kasting and 
Tbon 1989). The concept of the CHZ was introduced by Hart (1978, 1979). 


He defined it as that region of space in which a planet could remain 
habitable (i.e. maintain liquid water at its surface) over time scales long 
enough for life to originate and evolve. Hart concluded, based on what 
seems in retrospect to have been an overly simplified model, that the CHZ 
extended from only about 0.95 AU to 1.01 AU. In Hart's model, the inner 
boundary of the CHZ was determined to be the distance at which an Earth- 
like planet would experience a runaway greenhouse at some time during 
the last 4.6 billion years. The outer edge of the CHZ was the position at 
which runaway glaciation would occur. 

The climate models described earlier (Kasting 1988; Abe and Matsui 
1988) show that the runaway greenhouse threshold is considerably higher 
than Hart had estimated. If the minimum solar flux needed for runaway is 
1.4 So (see above), then the distance at which this would occur should be 
< 0.85 AU. On the other hand, the minimum solar flux required to lose 
water in the moist greenhouse model is only 1.1 S,,. The radial distance at 
which this might occur is thus 0.95 AU, in agreement with Hart's original 
estimate. Thus, it appears that Hart located the inner edge of the CHZ 
correctly, even though his reasoning was slightly flawed. 

The outer edge of the CHZ, on the other hand, probably lies well 
beyond Hart's estimate of 1.01 AU. Hart erred because he ignored the 
important feedback between atmospheric CO2 levels and climate (Walker et 
al. 1981). This story is told in detail elsewhere (Kasting et al. 1988; Kasting 
and Tbon 1989) and wiU not be repeated here. A modern conclusion, 
however, is that the CHZ is relatively wide, and that the chances of finding 
another Earth-like planet elsewhere in our galaxy are reasonably good. 


Runaway greenhouse atmospheres are much better understood than 
they were several years ago. Recent theoretical work has provided better es- 
timates of the amount of heating required to trigger runaway and new ideas 
about where such conditions may have applied. Future advances in our 
understanding of the evolution of Earth and Venus will require continued 
theoretical work in conjunction with new data on the isotopic composition 
of noble gases on both planets and on the water vapor distribution in 
Venus' lower atmosphere. 


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Earth's accretion. Icarus 74: 62-97. 


The Oort Cloud 

Leonid S. Marochnik, Lev M. Mukhin, and Roald Z. Sagdeev 
Institute of Space Research 


Views of the large-scale structure of the solar system, consisting of 
the Sun, the nine planets and their satellites, changed in 1950 when Oort 
(Oort 1950) demonstrated that a gigantic cloud of comets (the Oort cloud) 
is located on the periphery of the solar system. From the flow of observed 
comets of ~ 0.65 yr.~^ AU~^ the number of comets in the cloud was 
estimated at No ~ 2 - 10^ ^ Oort estimated that the semi-major axes of the 
orbits of comets belonging to the cloud must lie within the interval 4- 10'' 
AU < a ^ 2 • 10^ AU. This interval is now estimated to be 2-310'' < a 
< S-IOIO'* AU (see Marochnik et al. 1989). 

The original estimate of the Oort cloud's mass was made on the 
hypothesis that the nuclei of all comets are spherical with a mean radius 
value on the order of R = 1 kilometer and a density of p = P/cm^. This 
produced an Oort cloud mass of M^, = 0.1 M^ (Oort 1950). Therefore, 
the comet cloud that occupies the outer edge of the solar system appeared 
to be in a dynamically zero-gravity state, having no effect on the mass and 
angular momentum distribution in it. 

However, the estimate of the Oort cloud's mass was gradually increased 
(see below). We cannot rule out at this time the possibility that the Oort 
cloud has a concentration of mass comparable to the aggregate mass of 
the planets, in which the bulk of the solar system's angular momentum is 
concentrated (Marochnik et al. 1988). 




The value of N„ ~ 210" (Oort 1950) was yielded without accounting 
for observational selection. Everhart (1%7) was apparently the first to 
account for the effects of observational selection, having estimated the 
"true flux" of "fresh" comets as 4.7 yrs.-^ AU'^. This generated the 
estimate of N<, ~ 1.4101^. Monte Carlo modeUng of the dynamics of 
the Oort cloud's comets (Weissman 1982; Remy and Mingrad 1985) also 
yielded figures within the interval No = 1.2-210^^. 

Weissman's analysis (1983) of the mass spectrum of comets in the Oort 
cloud demonstrated that the increase in the number of comets by an order 
in comparison with the original estimate of the Oort cloud is primarily 
due to comets of low mass and a large absolute value of H". Accordmg 
to Weissman's estimate (1983), N, ~ I.21012 ^r comets whose absolute 
values are Hio < 11.5. With a density of nucleus matter p = I /cm and 
a surface albedo of A = 0.6, Weissman (1983) yielded Mo ^ 1.9 M®, 
an average mass on the spectrum for a typical comet of <Mu,> 7.310 g 
and a corresponding radius of the nucleus of <Ru.>^ 1-2 kilometers. In 
addition, No"'/<M^> 1.610'2. ^ 

Hughes (1987; 1988) however, demonstrated that Everhart s data 
(1967) had apparently been subjected to the effects of observational se- 
lection, since the index of the corresponding distribution function of long- 
period comets (LP) for absolute values (and, consequently, by mass; see 
below) is dependent upon perhelion distances and the epoch in which these 
comets are observed. If this is true, then doubt is cast over the estmiate 
based on Everhart's data (1967) of the number of comets in the Oort 
cloud, generated by extrapolating the observed flux in the region of the 
largest values. In this case, we must return to the estimate of No ~ 2 10 , 
obtained on the basis of direct obseivations, without taking into account 
the effects of observational selection. However, the mean mass of a typical 
"new" comet must also be estimated using direct observations, without 
extrapolation in the region of smaU dimensions and comet nucleus masses. 
Direct observations of 14 bare nuclei of long-period comets (i.e., 
observations at great heUocentric distances) produced, according to Roemer 
(1966) a mean radius of Rj^p = 4.2 kilometers. Similarly, a mean radius of 
RiP = 5.8 kilometers was found for 11 comets with bare nuclei, selected 
by Svoren (1987) from a total number of 67 long-period comets. Both of 
these Rlp values were yielded on thejiypothesis that the mean albedo of 
long-period comets A^p is equal to A^p = 0.6, in accordance withjhe 
computation done by Delsemme and Rud (1973). A nucleus mass of Mlp 
~ 510'^ at /? = 1 g/cm^ corresponds to the average of these two values 
of Rlp = 5 kilometers. For a more probable value of the density of the 
matter of a nucleus of p ~ 0.5 g/cm^ (Sagdeev et al. 1987) 



Mlp =; 2.5 • 10*^. (1) 

Analysis of the mass spectrum of long-period comets using Hughes data 
(1987, 1988), i.e., without taking into account the effects of observational 
selection, generates a mean LP-comet mass for the spectrum (Marochnik 
et al. 1989) of, 

<MLP>~1.2 10>^ff, (2) 

this virtually (with an areuracy to a factor of ~ 2) coincides with (1) - 
and the mean values of IAlp according to^ observations of bare nuclei of 
LP-comets with the same albedo value of Alp = 0.6. 

The closeness of the mean spectrum value < M^p > to the mean 
observed value Mip is understandable in this case (as opposed to the 
case where the effects of observational selection are taken into account). 
Actually, in hypothesizing the effect of observational selection, we find the 
number of comets in the Oort cloud N^ to be an order greater than directly 
follows from the value for the flux of observed LP-comets (see above), due 
to low-mass comets of low luminosity. This should considerably reduce the 
value < Mip > as compared with M^p. The fact that this is true can be 
seen by comparing the value Weissman generated (1983) of < M^p > = 
7.310^^g with (1). At the same time, when we only use the flux of observed 
comets, it is clear that < M^p > and Mlp cannot differ so greatly, which 
follows from comparing (1) and (2). 

At the same time, estimates of the Oort cloud mass Mo in both 
instances differ little since, despite the fact that the value of < Mlp > 
according to (2) is an order greater than < Mfp >, N<, is an order less 
than N^. A direct estimate based on (2) gives us: 

Mo = No- < Mlp >= 2 ■ lO" • 1.2 • 10"'(7 ~ 4M, (3) 

which is approximately twice as large as M^ generated by Weissman (1983). 
It is, however, a value of the same order. Therefore, if we refrain from 
"battling" for exactness in the coefficient values on the order of two (which 
is completely unjustified with the framework of ambiguities in observed 
data), we can then conclude that both approaches (accounting for and not 
accounting for the effect of observational selection) produce values of one 
order for the Oort cloud mass ofM„ ~ 2-4 M®, with a mean albedo of the 
nuclei of long-period comets of A^p 0.6. 

At the same time, direct measurements of the albedo of Halley's 
comet give us an albedo value of A// - 0.04+^°^ (Sagdeev et al. 1986). 
If we hypothesize that comets in the Oort cloud have an albedo which 
on the average approaches A//, then this must lead to an appreciable 


overestimation of the mass of M„. Since the mass of the nucleus of a 
comet is M ~ A'^f^, reduction of albedo by 0.04/0.6 = 1/15 times triggers 
an increase in the mass of the average comet and consequently, the mass of 
the entire Oort cloud by (15)3/2 ~ 58 times. Naturally, this must produce 
radical cosmogonic consequences. We will note that this cjrcumstance was 
first noticed by Weissman (1986). Having assumed that Alp = 0.05, he 
found that M,, ~ 25 M^. The corresponding estimate by Marochnik et al. 
(1988) produced M<, ~ 100 M®. _ 

What is the reasoning for hypothesizing that the values of Alp and 
Ah are approximately equal? 

We will first of all note that the mass of the "mean" short-period (SP) 
comet cannot be greater than the mass of the "mean" LP-comet. That is, 
the following ratios must be fulfilled: 

ULptMsp;<MLP> }:. <Msp>, (4) 

if, of course, we do not presuppose that LP- and SP-comets have varying 
origins (Marochnik et al. 1988). This study demonstrated that the measure- 
ments made during the Vega mission of the mass and albedo of Halley's 
comet (Mi/ and Ah) are typical for SP-comets, and approach the mean 
values of: 

Ah =i Asp ci 0.04, (5) 

Mh;^Mspc=;3 10^^. 

At the same time, an estimate of the loss of mass by Halley's comet 
during its lifetime has demonstrated that its initial mass was, probably, an 
order greater than its contemporary mass (Marochnik et al. 1989) and this 
(owing to Mh's convergence with typical mass values for SP-comets) allows 
us to hypothesize that the mean mass of a comet in the Oort cloud must 
be, apparently, at least an order greater than the present values of Msp 
and < M5P > in accordance with (4). 

On the other hand, according to Hughes (1987; 1988), the functions 
of comet distribution by their absolute values for LP- and SP-comets are 
homologous. In other words, the cumulative number of comets Nc„m(Hio) 
(i.e., the aggregate number of comets whose absolute values of < Hio) for 
LP-'and SP-comets have the appearance in the logarithmic scale of straight 
lines of equal inclination up to the corresponding inflection points in the 
spectra. These "knees" in the spectra of LP- and SP-comets have values 
of H^/ = 5.8 and H^^ = 10.8, respectively (Hughes 1987). In the regions 
of Hfo^ > H^^ and Hf(f > H^^, "saturation" occurs: the curves acquire 
a very gentle slope. The values of H^^ and H^^ are close to the mean 



value for the spectra, and in the regions Hf(f < H^^ and Hfo^ < H^^ the 
effects of observational selection are minor. 

The relationship between the absolute values of Hjo and the masses 
of LP- and SP-comets were explored by a number of authors (Allen 1973; 
Opik 1973; Newburn 1980; Whipple 1975; Weissman 1983). 

We will use Weissman's data (1983) who produced the following de- 
pendency from Roemer's data (1966) for LP- and SP-comets: 

logMLP = l9-OAHio + ^logl ^ j + \og{p/lg/cm^) (5a) 

logMsP = 20.5 - 0.37/10 + |/o</ (j~) + \og{p/lg/cm^). (56) 

From (5a) we find the ratios of masses corresponding to the "knees" in the 
LP- and SP-comet spectra to be equal to: 

It clearly follows from (6) that the albedo value of A^p = 0.6, assumed for 
LP- comets, directly contradicts (4). Formula (6) can be rewritten as: 



Therefore, the mean mass of LP-comets can only be an order greater than 
the mean current mass of SP-comets on the condition that 

Alp ~ 'Ksp- (8) 

We will note that there are also physical reasons for hypothesizing 
the close values of Alp and Asp. A low albedo is a consequence of 
the formation of a thin layer of dark material on the surface of the comet 
nucleus. Data from laboratory experiments on irradiation by energy protons 
of low-temperature ices (that contain H2O, CH4, and organic residues) 
demonstrate the formation of a black graphite-like material (Strazzula 

As Weissman has pointed out (1986b), the effect of galactic cosmic 
rays on comet nuclei in the Oort cloud (before their appearance in the 
region of the planetary system) must, for the aforementioned reason, lead 
to the formation of a sufficiently thick crust from the dark, graphite-like 


polymer. The latter acts as a "cometary paste" binding the nucleus surface 
against sublimation. 

It is our view that owing to the low heat conductivity of this polymer 
layer, a low albedo of the surface of comet nuclei can be maintained by 
a layer thickness of several centimeters. Due to the low volatiUty of this 
layer and its "sticky properties," the latter must also be conserved as the 
comet shifts into a short-period orbit. 

Therefore, if we are to propose that the hypothesis (8) is correct, we 
can estimate the mass of the Oort cloud to be a value of M<, ~ 100 M^ 
(with an accuracy of up to a factor on the order of two). 


It has currently been deemed likely that the canonical Oort cloud 
is only a halo surrounding a dense, internal cometary cloud. This cloud 
contains one to two orders of cometary nuclei greater than the halo with 
an outer boundary corresponding to the semi-major axis, a^ = 2-310^ 
AU (Hills 1981; Heisler and TVemaine 1986). It is a source which delivers 
comets to the halo as the latter is depleted when the Sun approaches closely 
passing stars and gigantic molecular complexes in the galaxy (GMC) and 
under the impact of the galactic tidal effects. The internal cometary cloud 
is sometimes called the Hills cloud. The outer boundary of the Hills cloud 
is defined quite clearly, as Hills demonstrated (1981), since comets with 
semi-major axes of a < a= do not fill the loss cone in the velocity space 
delivering them to the planetary system region of the solar system, where 
they have been recorded through observation. According to Hills, the 
value of il is weakly dependent on the parameters input into the formula 
to determine this value (an indicator of the degree of 2/7). Therefore, the 
value of al ~ 2- 10^ AU is defined with sufficient certainty. Bailey (1986) 
also later generated the same \^lue for the outer inner cometary cloud 
(ICC) boundary prior to this; he considered interaction with GMC instead 
of convergence with stars, as Hills had done. Furthermore, if the tidal 
effect of the "galaxy's vertical gravitational pull" is taken into account, we 
have, according to Heisler and TVemaine (1986) an estimate of a^ ~ 3 Iff* 


The location of the inner boundary of a? is considerably less definite. 
An extreme estimate, performed by Whipple (1964) produces a? > 50 AU. 
At the same time, by hypothesizing that comets are formed in the outer 
regions of the protosolar nebula. Hills (1981) estimated the inner boundary 
of the core as a? ~ 3- 10^ AU. 

What is the mass of the Hills cloud? Let us designate the number of 
comets in it as N^cre, so that 



iVcore = P-K. (9a) 


M„„ = PM„, (96) 

where the value of p is not clearly known. 

What can be said about the value of /3? Simple extrapolation for the 
core of the law of comet distribution around the semi-major axis in the 
halo for the original Oort model and a somewhat refined version produce, 
according to Hills' estimate (1981), ^ = 20 and /? = 89, respectively. 

Proposing that comet formation occurs in the Uranus-Neptune zone, 
Shoemaker and Wolfe (1984) and Duncan et al. (1988) generated /? = 
10 and /3 = 5, respectively, in their numerical experiments. The internal 
boundary of the core in the latter instance was equal to 310^ AU; this fits 
with Hills' estimate (1981). 

However, it was proposed in these computations that the total mass of 
comets scattered by Uranus and Neptune is minor when compared with the 
masses of the planets. Clearly, this is not true if the reasoning put forward 
in this paper is sound. For this reason, the results generated by the authors 
mentioned here apparently require clarification. 

Assuming, nevertheless, the region of parameter alteration as: 

/? = 5-10, (10) 

we find the mass of the Hills cloud approximately 

A^core ::; 500-1 OOOM0. (H) 

Figure 1 represents schematically the probable mass distribution in the 
solar system for ^ = 10, in the case of a massive Oort cloud. 


If the Hills and Oort clouds are truly as massive as follows from the 
above estimations, then: (1) comet formation could hardly have occurred in 
the Uranus-Neptune zone, as is frequently considered, since as such a large 
mass was ejected to the periphery of the solar system, the planets should 
have moved considerably closer to the Sun (Marochnik et al. 1989); (2) 
since comet formation apparently took place in the rotating protoplanetary 
disk (if, of course, we rule out the hypothesis of cometary cloud capture 
during the Sun's formation through GMC) (Clube and Napier 1982), then 
since the angular momentum is conserved, the greater portion of it must. 




102 10^ 

Heliocentric distance 



FIGURE 1 Histogram of the probable mass distribution in the solar system. A planeury 
system with a mass of EMp/ane. = 448 M® is located in the region of heliocentiic 
distances where r < 40 AU. The Oott cloud with a mass of M^ ~ 100 M® is located m 
the zone of ZlC < r < 510'' AU. A Hills cloud with a mass of Mcort ^ 10^ M^ is 
located In the region where r < aW AU. The internal boundary r;"^ of the Hills cloud 
is ambiguous. According to data from Hills (1981) and Duncan el al. (1988), u" ~ 310^ 
AU. However, neither can we exclude the value r,'= ~ 50 AU (Whipple 1964). 

apparently, be concentrated in the massive Oort and Hills clouds, and not 

the planets. 

According to Marochnik et al. (1988) the Oort cloud's angular mo- 
mentum can be written as 

J, = 4/3M„(GMQa„i„)^/='(l + «-'/') - 1, 


where the original Oort model is used (Oort 1950) for the function of 
comet distribution by energies (n = 2); a = Omaxl amin, «m.n and Omai 
denote the minimum and maximum possible semi-major axes of cometary 
orbits. Since the Oort cloud is thermalized by passing stars, integration 
occurs in (12) for aU possible eccentricities (0 < e < 1). 

Assuming that M„ = 100 M®, «„;„ = 210" AU, a„„ = SIO^ AU, 
we find that 

J„ = 3 • 10"ff ■ cm? Is. 



For the assumed parameter values, the angular momentum of the halo is 
on the same order as the minimum possible angular momentum of the 
protosolar nebula before it loses its volatiles (Hoyle 1960; Kusaker et al. 
1970; Weidenschilling 1977) and an order greater than the present angular 
momentum of the planetary system. EJpianct ^ 3 lO^^g cm^/s. Estimate 
(13) fits with the hypothesis of the in situ formation of comets, and thus 
generates the upper limit of the Oort cloud's possible angular momentum. 
The lower limit will clearly be seen if we suppose that comet formation 
occurred in the Uranus-Neptune zone. Assuming, for example, that a^in = 
25 AU, Qmax = 35 AU, and supposing that the initial comet orbits in this 
case are nonthermalized and circular, we find that 

Jo = 1.5 • I0^°gcm^/s. 

Therefore, the interval in which Oort cloud angular momentum may 
lie can be written as: 

1.5 • 10^°gcm^/s < J, < 3 • lO^^gcm^/s. (14) 

In any case, as we have seen: 

Jo r^'EJplanet- (15) 

Let us now estimate the angular momentum for the Hills cloud. Since 
it is apparently nonthermalized, its angular momentum J^ore is equal to 
(Marochnik et al. 1989): 

Jcor. = 2M„„[GA/0a^,„(l - e2)]i/2(l + a^'f')-', (16) 

where, as in conclusion (12), the classical Oort model is used: (n = 2), 
a^,„ and Oc modify the core. 

Let us consider two extreme cases: (a) all the comets in the Hills cloud 
move along circular Kepler orbits (e = 0), and (b) all the comets in it move 
along sharply elongated, circumparabolic orbits (e < 1). In the case where 
e = 0, assuming M„re ^ 10^ M®, a^,„ = SIO^ AU, a^„ = Zlff" AU, 
we find: 

J.ore =i 2 • 10^5 • cm Vs- (17). 

Estimate (17) agrees with the suggestion that comets are formed in situ and 
gives us an upper limit for the value J„r« (for estimating the momentum, 
present values of a^.„ and a^„^ are used). In the case where e £ 1, we 
need to rewrite (16) in terms of perihelion distances of q = a(l - e), that 
is, using the ratio 

(^minii-e'')c:^2q,„in, (18) 


J (g cm2/s) 
_ 1052 - 










10 102 103 

Heliocentric distance 




FIGURE 2 Histogram of the probable distribution of angular momentum in the solar 
system. A cometary system with a total angular momentum of SJp/anet = 3- 10 is 
located in the region of heliocentric distances of r < 40 AU. An Oort cloud with a mass of 
Mo = 100 M^ and angular momentum of J^, = 1.510 g cm /s is situated m the zone 
of ZIO"* < r < 510'' AU. A Hills cloud with a mass of More = 500 M^, an internal 
boundary that is ambiguous (50 ^ rj*^ ^ 310^ AU) and an angular momentum of 
Jcore = 310^' gcm^/s is located in the zone of r < ZIO'' AU. 

where qmin denotes the perihelion distances of the comets' cores, which 
have minimum semi-major axes am.n'^- The lower hmit for Jcore can be 
produced, supposing that the formation of the comets of the Hills cloud 
occurred in the Uranus-Neptune zone. Assuming that qmin ^ 25 AU, we 
find from (16), and taking into account (18), that: 

Jcore - 3 • lO^^ffcmV*. 

Therefore, for the angular momentum of Jcore, we can write the following 

o ' lU v!. Jcore 

V 103 Me 

< 2 • 10 

52 9 cm^ 


The angular momentum of Jcore is, therefore, very large: one to two 
orders greater than the contemporary angular momentum of the entire 
planetary system EJpjanei- However, its value still does not exceed the 
limits of the upper estimate of the possible initial angular momentum of 
the protosolar nebula (Marochnik et al. 1988). 

Figure 2 shows angular momentum distribution in the solar system in 
the case where the Oort and Hills (/? = 5) clouds are not too massive. 



The picture we have described of the structure of the solar system 
apparently does not contradict IRAS data on observations of infrared 
excesses in stars of the circumsolar vicinity of the galaxy. 

As Backman notes (personal communication), IRAS data shows that 
thin clouds of solid particles are spread out over distances of up to 700 
AU near the stars a Lyrae and /? Pictoris, and, possibly, up to 10* AU, 

According to Smith's data (1987), optical observations of P Pictoris 
point to the presence around this star of an elongated (radius ~ 11^" AU) 
and a thin (projected thickness is h ~ 50 AU) disk. According to data from 
Smith and Tferrile (1984), optical observations of p Pictoris may also be 
evidence of the presence of a zone of transparency with a radius of about 
30 AU around this star. 

Of the 150 main sequence stars in Glize's catalogue, and which were 
examined by Backman (1987), 18% demonstrated infrared excess at a level 
of 5 sigma. This exceeds the extrapolated photospheric flow. According to 
Backman's analysis (1987), this may indicate the presence of thin clouds 
of solid particles spread out over distances of 10 + 1000 AU from the 
respective stars. 

The presence of elongated disks of fine solid particles spread out over 
distances of hundreds and thousands of AU from the respective stars is 
most likely evidence of the presence in these regions of bodies of cometary 
dimensions for which the sublimation of volatiles and mutual collisions 
may ofliset the accretion of dust grains from these regions by light pressure 
and the Poyting-Robertson effect during the lifespan of a star (Weissman 
1984; Harper et al. 1984; O'Dell 1986). As Beichman has noted (1987), the 
masses of disks around the stars are apparently the most difficult values to 
determine. A huge spread in estimates exists for /? Pictoris: from Md„t 
~ 10~^ M® for dust grains of equal dimensions to Mdi,t ~ 3 lO^M® for 
an asteroid-like distribution of them (Aumann et al. 1984; Weissman 1984; 
Gillet 1986). 

Therefore, the data of infrared observations of stars near the solar 
vicinity of the galaxy do not apparently clash with the proposed model 
of the structure of the solar system. Attempts to make some stronger 
assertions would be too speculative at this point. 


Assuming as typical for long-period comets the albedo value of Halley's 
comet, we come to the conclusion that the Oort cloud must be extremely 


massive (M^, ~ 100 M®). This mass must be located in the region of the 
semi-major axes of the orbits: 

2 - 3 • 10'* AU < a < 5 - 10 ■ lOMC/. 

The hypothetical Hills cloud is located in the region a < 2- 310^ 
AU. It has a mass of M^ore = P^o, where the value P may generally be 
included in the ranges of < ^9 < 100. 

The extreme case of /? = fits with the general hypothesis of the 
absence of the Hills cloud. The case where /3 = 100 agrees with the other 
extreme hypothesis of the highly massive core. 

In limiting ourselves to the values of /? = 5 - 10, we find the Hills 
cloud mass of Mcore = 500 - 1000 M^, which must have a value of a^ = 
2-310^ AU as an outer border. The internal boundary of the Hills cloud 
is indefinite. 

Therefore, the hypothesis of the low value for the albedo of comets 
in the Oort cloud brings us to the conclusion that at the outer edge of the 
solar system there may be an invisible material in the form of cometaiy 
nuclei whose mass, TMcomet- 

'^Mcomet ~ ^Mpianet, (20) 

where E Mp/oneJ denotes the total mass of the planetary system. 

The second conclusion states that the cometary population, and not 
the planetary system accounts for the bulk of the solar system's angular 
momentum. On the basis of (14) and (19) we can write the following, 
which is analogous to (20): 

where TiJcomet denotes the total angular momentum of the cometaiy pop- 
ulation. Let us note in conclusion that if (20) and (21) are correct, the 
cosmogonic scenarios for the solar system's origin call for considerable 


We are deeply grateful to Alan Boss and Paul Weissman for their 
important comments, and to Vasilii Moroz and Vladimir Strel'nitskii for 
their insightful discussion, and to Georgii Zaslavskiy for his input regarding 
individual aspects of this study. 


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diversity and similarity of comets 6-9 April. Brussels, Belgium. 
Weidenschilling, S. 1977. Astrophys. Space Sd. 51:153. 
Weissman, P.R. 1982. Page 637. In: Wilkening, L. (ed.). Comets. University of Arizona 

Press, Tlicson. 
Weissman, PR. 1983. Astron. Astrophys. 118:90. 
Weissman, PR. 1984. Sdence 224:987. 
Weissman, PR. 1986a. Bull. Am. Astron. Soc. 18:799. 
Wsissman, PR. 1986b. ESA SP-249. 
Whipple, EL. 1964. Ptoc. Nat. Acad. Sd. USA 51:711. 
Whipple, EL. 1975. Astron. J. 80:525. 


The Chaotic Dynamics of Comets and the 
Problems of the Oort Cloud 

RoALD Z. Sagdeev and G.M. Zaslavskiy 
Institute of Space Research 


This paper discusses the dynamic properties of comets entering the 
planetary zone from the Oort cloud. Even a very slight influence of the 
large planets (Jupiter and Saturn) can trigger stochastic cometary dynamics. 
Multiple interactions of comets with the large planets produce diffusion of 
the parameters of cometary orbits and a mean increase in the semi-major 
axis of comets. Comets are lifted towards the Oort cloud, where collisions 
with stars begin to play a substantial role. The transport of comets differs 
greatly from the customary law of diffusion and noticeably decelerates the 
average comet flow. The vertical tidal effect of the galaxy in this region of 
motion is adiabatic and cannot noticeably alter cometary distribution. A 
study of the sum of forces operating in the region to a ~ IC AU does not 
permit us to explain at this time the existence of a sharp maximum, where 
a ~ l{y AU in the distribution of long-period comets. This is an argument 
in favor of the suggestion that it was caused by the close passage of a star 
several million years ago. 


The solar system's new object, the Oort cloud, arose as a source of 
long-period comets (Oort 1950) in the planetary system's visible portion (r 
< 2 AU). Experimental material generated by processing the trajectory of 
a large number of long-period comets (Marsden et al. 1978; Marsden and 
Roemer 1982) determined for these comets the region in which they exist, 
which reaches a size of up to ;S 210^ AU. Oort proposed that collisions 



with Stars passing fairly close to the Sun may be one of the primary causes 
for which comets attain the visible region. Research during the ensuing 
years greatly complicated the Oort cloud model, inputting Hills cloud (Hills 
1981) into the analysis (with an upper boundary of r ~ 2- 10^ AU) and the 
action of various forces such as the galactic tidal effect (Hills 1981; Heisler 
and TYemaine 1986; Morris and Muller 1986; Bailey 1986), collision with 
molecular clouds (Biermann and Lust 1978; Hut and Tl-emaine 1985), and 
interaction with the planets (Oort 1950; Khiper 1951). 

Numerical analysis within the framework of the simplest, initial Oort 
model demonstrated the possibility of qualitatively explaining the reason 
for which comets enter the visible zone due to the effect of near stellar 
passages (Wiesmann 1982). Subsequent analysis showed that the action of 
the galaxy's vertical tidal effect may somewhat modify Oort cloud and Hills 
cloud parameters and the number of comets in them (Fernandez and Ip 
1987; Duncan et al. 1988). Oort cloud mass and momentum may fluctuate 
more significantly if we assume certain, typical estimates for them, made 
after processing the results of the Halley's comet mission (Marochnik et al. 
1988). The large mass of the Oort cloud (M,, ~ 100 M^, r > 210'' AU) 
must affect in the most serious way models of the formation of the solar 

It should be added here that the increase in the mass of the Hilk cloud 
must also bring about an increase in its angular momentum (Marochnik 
et al. 1988). This must be reconciled with the approximate equality of the 
number of prograde and retrograde new comets. If it was not a question 
of new comets, this equality would be a sufficientty obvious consequence of 
the impact of random collisions of stars with comets with highly eccentric 
orbits. However, numerical simulation, where the initial angular momen- 
tum value of the cometary protocloud is taken into account, also reveals 
the considerable impact it exerts on the size of the final Oort cloud and on 
the number of comets in it (Lopatnikov et al. 1989). The obvious reason 
for this is tied to the different impacts of stellar collisions on circular and 
eccentric orbits. 

In accounting for the final angular momentum of cometary distribution 
in the Hills and Oort clouds, an anisotropy is created in cometaiy dynamics 
at virtually all of its stages. Anisotropy in the distribution of cometary 
aphelia has been experimentally discovered (Delsemme 1987). It indicates 
the correlation between cometary distribution and the effect of galactic 
tidal forces. We can consider that these forces exert an influence on both 
cometary dynamics in the aphelion region (Heisler et al. 1987) and on 
their dynamics in the planetary zone. Hence, all characteristic regions of 
cometary orbits must participate in an interrelated manner in the formation 
of cometary zones. This makes it necessary to analyze more carefuUy all of 
the processes by which comets interact with the planets and the stars. 


The interaction of comets with the stars is statistical. Therefore, the 
impact of individual collisions is averaged out, while the mechanism itself 
by which they have an impact on the zone of cometary aphelia is weakly 
dependent on individual details. 

The passage of comets through the planetary zone is quite different. 
The influence of the large planets, Jupiter and Saturn, on cometary dy- 
namics has proven more subtle. A significant portion of comets (about 
50%) which pass close to Jupiter are thrown into hyperbolic orbits as early 
as the first passage. However, the phase space occupied by comets with 
a perhelion < 2 AU is not very large. The phase space occupied by 
comets with a perihelion similar to the radius of Jupiter's orbit is sub- 
stantially greater. The phenomena of chaos may arise for such comets 
(Petroslq' 1986; Sagdeev and Zaslavskiy 1987; Petrosky and Broucke 1988; 
Sagdeev et al. 1988). They consist of the following: in the strictly dynamic, 
three-body problem (Sun-Jupiter-comet), the movement of the comets in 
varying conditions becomes unstable. This instability is seen, in particu- 
lar, in the fact that Jupiter's phase at the moment when a comet passes 
through its perihelion is a sequence of random numbers. As a result, a 
mechanism accelerating comets begins to operate. This mechanism is anal- 
ogous to Fermi's method of stochastic acceleration (Sagdeev et al. 1988). 
It produces diffusive alteration of all of the comet's parameters, a mean 
increase of the semi-major axis of cometary orbit, and the expulsion of the 
comet from the solar system. The process of stochastization of cometary 
movement is considered in detail in Natenson et al. (1989). Numerical 
analysis demonstrated that the region of cometary eccentricity values for 
which chaos arises is very broad. Orbits with c ~ 0.5 may already become 
stochastic. This circumstance should noticeably modify views of cometary 
interaction with the planetary zone. 

We will discuss below the conditions in which the dynamics of comets 
with long-period orbits become stochastic, the role of such comets in the 
overall model of the Oort cloud, and the influence of the galactic tidal 
forces on cometary dynamics. 


We can generate a straightforward idea of this chaos by looking at 
how a ball falls on a heavy plate in a gravity field (Figure 1, Zaslavskiy 
1985) and if we consider their collision to be absolutely elastic. If the plate 
oscillates with an oscillation amplitude of a and a velocity amplitude of v, 
then on the condition that: 

2tJ^ > ag, 
(g denotes acceleration in the gravity field), the oscillation phase of the 




FIGURE 1 Illustration of the action of the "gravitational machine" (Zaslavskiy 1985), 
triggering the stochastic increase of the energy of a ball bouncing on a periodically oscillating 

plate at the moment of collision is random. The ball bounces irregularly 
over the plate and, on the average, rises increasingly higher. Its mean 
energy at the moment of impact behaves asymptotically, as in <v^ > ~ 
l^/^, and the mean height of lift correspondingly increases, as in <h^ > ~ 
1^/3. The time for the ball to return back to the plate, naturally, increases. 
However, the acceleration process does not stop. 

This example somewhat clarifies what occurs with long-period comets 
whose perihelion is in the sphere of influence of, for example, Jupiter. 
Let M denote the orbital momentum of a comet, and V be the phase of 
a comet's location relative to Jupiter in the comet's orbital plane. If the 
orbits of Jupiter and the comet lie in the same plane (the so-called flat, 
limited three-body problem), the Hamiltonian for the comet is equal to 



(7 = ± 1 defines here either prograde or retrograde comets; /i denotes the 
ratio of Jupiter's mass to that of the Sun; 

n = [r^ -f- 2/ir cos{'p - awjt) + fi^f^^ 

'■2 = P - 2(1 - fi)r cos{<p - <jwjt) -f (1 - liff'^, 

where the radius of Jupiter's orbit, Xj, is assumed to be equal to the 


unit, wj (Jupiter's rotational frequency). In this two-dimensional motion, 
ip = rp - <rwjt, and a Jacoby motion integral exists: 

Go^H- awjM. (2) 

Using ratio (2), we can make problem (1) a two-variable, nonstationary 
problem. We can select a canonically coupled pair (M, ^) as the variables. 
Let, for example, t„ denote the moment in time when the comet passes 
through its aphelion, M„ be the orbital momentum during passage through 
aphelion, and Vn denote the value of the Jovian phase during cometary 
passage through perihelion (preceding the time t„). The relationship be- 
tween the values (M„+i, Vn+i) and M„, ^„) then defines the expression 
(Petrosky 1986; Sagdeev and Zaslavskiy 1987) 

Mn+i = M„ + AM sinipn (3) 

V'n + l = V'r. + 25rO-— -, 

where AM denotes fluctuation in the orbital momentum over one cometary 
rotation, while the comet's energy, E„ is determined using the motion 
integral (2): 

En = Go + <rwjM„. (4) 

The variables (M„, ^n) are canonically coupled. Expression (3) is only 
defined in the region of negative values of a comet's energy, H = E < 0, 
that is , according to (2) 

Go + (rwjM <0. (5) 

Inequality (5) is violated and expression (3) becomes meaningless when a 
comet is thrown into hyperbolic orbit The value AM in (3) is defined by 
the expression 

/'•+» dH 
AM = max / dt-—-, (6) 

where t„, and t„+i denote the moments of time of two sequential passages 
of the apocenter by a comet. Estimates of the value of AM in vaiying cases 
are provided in Petrosky 1986; Sagdeev and Zaslavskiy 1987; Petroslq' and 
Broucke 1988; Natenson et al. 1989. 

Expression (3) has a frequently encountered form, described in detail 
by Sagdeev et al. (1988) and Zaslavskiy (1985). If a comet does not pass 
too far from Jupiter, the duration of its interaction with Jupiter is on the 
order of a Jovian period of 2n/wj. This time scale determines the duration 


of a "collision." It is a great deal less than the time period between two 
"collisions" for long-period comets of 2irfw(E). In view of this circumstance, 
we can write a simple form of expression (3), in which the second formula 
simply describes alteration of the V phase during the time between two 
sequential collisions. A similar expression also occurs for the model with 
the ball in Figure 1. The velocity, v, plays the role of a generalized pulse, 
M, while the collision frequency is proportional to lA'. In this case, w(E) 
= |2£p/2. 

We can produce a straightforward assessment of the stochastic dynam- 
ics of the comet for problem (3) from the condition that (Sagdeev et al. 
1988; Zaslavskiy 1985): 

K = 
This gives us 

A = 2ir- 






1 >1. (7) 

|AMcost/i| > 1. (8) 

Since the perihelion changes little as a result of the collision (AM 
< M), while the comet's rotation frequency w(E) = | 2E|^/^ — ► where 
|E| -+ 0, condition (8) can be fulfilled for comets with sufficiently low 
binding energy (|E| — * 0) with a fixed value M. The phase portrait of 
cometary movement, corresponding to the Hamiltonian (1), with a fixed 
Jacoby integral value is in Figure 2 (Natenson et al. 1989). It was produced 
for true trajectories and demonstrates the complex structure of phase space 
with a large number of regions of stability. TTie region of global chaos is 
defined by the estimate in (7) and (8). A boundary with c m 0.55 and a 
semi-major axis of a « 16.5 AU corresponds to this. The comet's perihelion 
originally had a value of q « 7.5 AU. 

Points in the region of global chaos in Figure 2, that is where < 
E < - 0.03 AU, belong to one trajectory. If any initial condition in this 
region is selected, with the same Jacoby integral value, the corresponding 
movement of a comet will also be stochastic. This is where the significance 
of this region of stochasticity is manifested. 

TWo important consequences stem from the results of study (Natenson 
et al. 1989). The region of chaos is very significant, and even Halley's comet 
enters the zone where conditions of chaos are applicable. An analogous 
comment regarding Halley's comet, based on the use of representation 
(3), was made by Chirikov and Vecheslavov (1985). The region of chaos 
in Figure 2 also applies to medium-period comets. Therefore, the phase 
magnitude of comets with stochastic dynamics is an order more than the 
phase magnitude of comets appearing in the visible portion with r < 2 AU. 









■:?f .■i.,i».,.i ' 

-7.''i-" ;;:.■.. I-,:,,.-:. ^.u,.-,i-»^-,yx; .■■y',.:i-..'...7;.r>'.(-, -,.■.■, :!>< k:-^ .■-> 
*£^- 'jSi S'-i ' ■ »•■ i : - ■ Mii-'Vf : -v ^ ■ ■ ; ; . J7^^ ^ *jpia ie.'»:J .<..:i^ 



■ •.'■"■ "^V'-' . 


,-•:'• -;•■•;■■■•;-'■■•'' ■■■■>.■: i • 'r'.-'<...\...;;.-*::,M 'v .■'-:■■;.:<-■) • J-r."".--'-! 

, .-ri'-'i-^Ji: ■■■: ..'l•:'•.•■'V■'^^'•''<■-' ■■■'■■-■■-:-■.-■? ••'. ■...■.■:■■-■ -:-.-.'-i ■' 
■•"■■'.■■ ;'f-/.v:i ■■ V' ■:•.: ^-.-.i- ,- .^ i'.;.---.-..,.. < .-•S' ..i>,' .;::, f.-,. ,'V; '..-'. :'. ; >■ ! -■'- 


FIGURE 2 Phase portrait on the trajectory plane (ip, E = — l/2a) of a comet. The orbit 
points are plotted at the moment in time when a comet passes through the apheUon point. 
For the sal;e of convenience, the portrait has been broken into two parts. 


The second consequence is related to the nature of cometary diffusion. 
This process is extremely important, since it is the mechanism by which 
comets attain the region of semi-major axes. The usual diffusion formula 
(Yabushita 1980) 

is only justified in a region sufficiently remote from the chaos boundary. 
The impact of the chaos boundary and regions of stability (see Figure 2) 
significantly decelerates diffusion at the initial stage in comparison with the 
diffusion defined by formula (9) (Natenson et al. 1989). 


The existence of a mechanism of dynamic chaos makes it necessary 
to reconsider the general dynamics of comets as they move from the Oort 
cloud to the visible zone. The customary route is that collisions with stars 
operate in the zone of aphelion of a comet's orbit. Those comets in the 
loss cone region enter the visible zone, originally having a ^ 10^ AU. 
Jupiter's influence throws about one half of these comets into hyperbolic 
orbit. Only a small portion of the comets may subsequently return again 
directly to the loss cone, in order to set out on the new path from the Oort 
cloud to the visible zone. 

However, another avenue also exists. 

A rather large portion of comets, those that first entered the invisible 
zone and have a perihelion comparable to the radius of Jupiter's orbit, 
enter the region of stochastic dynamics. The comet begins a long, diffusive 
path to the loss cone region. Therefore, an independent way of filling the 
loss cone is defined. 

Other large planets of the solar system may also play the same role 
as Jupiter. Therefore, the portion of comets moving stochastically should 
be insignificant. The planetary "barrier," expelling part of the comets, 
concurrently makes the dynamics of others stochastic, thereby providing 
their route to the loss- cone. At the same time, the cometary perihelion 
changes very slightly, and the comets' orbits are as if "attached" in the zone 
of their perihelion. 

Vertical tidal galactic forces must play an important role in the process 
of cometaiy stochastic transport described above (Bahcall 1984; Heisler 
and TVemaine 1986) 

F, = lirmG/),z, (10) 


where m denotes comet mass, G is the gravitational constant, p& = 0.186 
mo/pc' is stellar density, and z is the vertical coordinate in the galactic sys- 
tem of coordinates. The tidal force (10) considerably alters the perihelion. 
Therefore, it creates the drift of comets from the planetary zone during 
one phase of cometary orbit and, inversely, causes cometaiy perihelia to 
flow into the planetary barrier in another orbital phase. These two fluxes 
are approximately equal. 

We will find the region, on the nonadiabatic influence of the tidal force 
F^, from the condition that perhelion variation under its influence must be 
fairly strong. We will assume 10 AU as an example of the characteristic 
size of the planetary zone. Then the nonadiabatic condition means that 

A9>10/lf/, (11) 

where Aq denotes perihelion alteration under the influence of F^ in a 
period of cometary orbit. For eccentric orbits 


Aq ~ MAM/m^mQG. 

AM ~ FtaT -^ ATtmGp.a^T ~ nmQGa^T/pc^, 
after substitution of all of these expressions in (11), we yield: 

a > 10" At/. 

This estimate (Duncan et al. 1988) can also be clarified using a more 
careful input of numbers. However, it is clear that the effect of tidal 
forces in the region of a significant portion of cometary orbits is adiabatic. 
Therefore, the tidal forces cannot substantially alter cometaiy distribution 
in the region ;$ 10" AU. However, they exert considerable influence on 
the near-boundary processes, where the planetary barrier operates, and 
along the border of the Oort cloud, where effective collisions with stars fill 
the loss cone (Fernandez and Ip 1987; Duncan et al. 1988). 


The dynamic chaos of comets with fairly eccentric orbits, moving in 
the Sun's field and perturbed by the fields of Jupiter and Saturn (or by the 
fields of other remote planets), forces us to reconsider individual elements 


of the Oorl cloud theory. Cometary stochastization creates a mechanism by 
which comets move away from the planetary belt towards the Oort cloud, 
and may be an additional source by which the loss cone is filled. The 
process of diffusive cometary transport differs from the usual process of 
diffusion and retards the characteristic time scale for the flux of comets 
toward the semi-major axes a. The action of the tidal forces does not 
alter this time scale significantly and is adiabatic (with the exception of the 
regions near the belt of the large planets and near the inner boundary of 
the Oort cloud). Therefore, the internal mechanisms of cometary dynamics 
cannot explain the existence of a sharp maximum in the distribution of 
the observed comets from the Oort cloud (Marsden et al. 1978; Weismann 
1982) with a period on the order of several million years. This gives us 
reason to suggest that the reason for the appearance of such comets may 
have been the last near-Earth passage of a star. This conclusion correlates 
with the conclusions of studies Biermann et al. 1983; Lust 1984) on the 
possible passage of a star or another large object in the region of cometary 
orbit with a ~ 10^ AU, triggering the appearance of a coherently moving 
cometary cluster. 

The global modeling of the dynamics of long-period comets must 
include the multiple interactions of comets with the large planets, if the 
perihelion of the comets does not greatly exceed the radii of planetary 
orbits. These issues and the existence of asymmetry in cometary cloud 
distribution are discussed in greater detail in Lopatnikov et al. (1989); 
Natenson et al. (1989). 


The authors wish to thank L.S. Marochnik, Al. Neishtadt, and P. 
Veismann for their useful comments. 


Bahcall, J.N. 1984. Aslrophys. J. 276:169. 

Bailey, M.E. 1986. Nature 324:350. 

Biermann, L., WF. Huebner, and R. Lusl. 1983. Proc Natl. Acad. Sci. USA 80:5151. 

Biermann, L,, and R. Lusl. 1978. Sitz. ber. Bayer. Akad. Wiss. Mat.-Naturw. Kl. 

Chirikov, B.V., and V.V. Vecheslavov. 1986. Preprint:86-184. Institute of Nuclear Physics. 

Delsemme, A.H. 1987. Astron. Astrophys. 187:913. 
Duncan M., T. Quinn, and S. Ttemaine. 1988. University of Tbronto. 
Fernandez, J.A., and W.H. Ip. 1987. Icarus 71:46. 
Heisler, J., and S. "ttemaine. 1986, Icanis 65:13. 
Heisler, J., S. Tlcmaine, and C Alcock. 1987. Icarus 70:269. 
Hills, J.G. 1981. Astron. J. 86:1730. 
Hut, P, and S. Ttemaine. 1985. Astron. J. 90:1548. 
Khiper, G.P. 1951. Page 357. In: Hynek, J.A. (ed.). Astrophysics. McGraw-Hill, New York. 


Lopatnikov, A., L.S. Marochnik, D.A. Usikov, R.Z. Sagdeev, and G.M. Zaslavskiy. 1989. 

Space Research Institute, Moscow, in press. 
Lust, R. 1984. Astron. Astrophys. 141:94. 

Marochnik, L.S., L.M. Mukhin, and R.Z. Sagdeev. 1988. Science 242:547. 
Marsden, B.G., Z. Sekanina, and E. Everhart. 1978. Astron. J., 83:64. 
Mar^len, B.G., and E. Roemer. 1982. Page 707. In: Wilkenlng, L. (ed.). Comets. The 

University of Arizona Press, Tlicson. 
Morris, D.E., and R.A. Muller. 1986. Icarus 65:1. 
Natenson, M.Ya., AI. Neishtadt, R.Z. Sagdeev, O.K. Setyakov, and G.M. Zaslavskiy. 1989. 

Space Research Institute, Moscow, in press. 
Oort, J.H. 1950. Bull. Astron. Inst. Neth. 11:91. 
Petrosky, T.Y. 1986. Phys. Lett. A. 117:328. 
Petrosl^, T.Y., and R. Broucke. 1988. Celestial Mechanics 42:53. 
Safronov, VS. 1%9. Evolution of the protoplanelary cloud and the formation of the Earth 

and the planets. Nauka, Moscow. 
Sagdeev, R.Z., D.A. Usikov, and G.M. Zaslavskiy. 1988. Nonlinear Physics. Harwood 

Academic Publishers, Chur. 
Sagdeev, R.V., and G.M. Zaslavskiy. 1987. Nuovo Cimento 97:119. 
Weismann, PR. 1982. Page 637. In: Wilkening, L.L. (ed.). CGmets. Arizona University 

Press, TUcson. 
Yabushita, S. 1980. Astron. Astrophys. 85:77. 
Zaslavskiy, G.M. 1985. Chaos in Dynamic Systems. Harwood Academic Publishers, Chur. 

N91-22980 . 

Progress in Extra-Solar Planet Detection 

Robert A. Brown 
Space Tfelescope Science Institute 


The solar system's existence poses this fundamental question: Are 
planetary systems a common by-product of star formation? One supporting 
argument is that flattened disks appear to be abundant around pre-main 
sequence stars (Strom et al. 1988). Perhaps the planetary orbits in the solar 
system preserve the form of such a disk that existed around the young 
Sun. Such heuristic evidence notwithstanding, real progress on the general 
question requires determining the frequency of occurrence of extra-solar 
planetary systems and measuring their characteristics (Black 1980). 

At the current time (the beginning of 1989) no investigator has an- 
nounced an extra-solar planet detection that is unqualified or that has 
been generally accepted as such. Indeed, the very definition of "planet" 
is ambiguous. The quest for planets is an arduous challenge — the classic 
astronomical grail. 

This paper reviews progress to date. Several observing programs have 
measured direct light from sub-stellar masses orbiting other stars. Those 
observations are helpful in understanding why planets have not been found 
by the same techniques: their visibility is very low as compared with more 
luminous bodies like brown dwarfs. 

Three investigator groups claim to have found evidence for smaller 
bodies, perhaps planets, by studying perturbations in star motions. Those 
observations are instructive about the specific strengths and weaknesses of 
indirect techniques for detecting planets with various masses and orbits. 

More capable extra-solar planet searches are being planned for the 




(B 3 
















o w 

0.063 - 

0.032 - 


c ® 





$ T 




- Giclas 29-38 b 
^- Gliese 569 B 


!->• Hydrogen Burning 
■H "Wof formed like stars " 
"Not unlike Solar System planets" 

log r- 

Solar Mass -4 






-1 1 1 

1 2 

n log 

3 Jupiter Mass 

FIGURE 1 Mass-radius spectnim for planets, brown dwarfs, and stars. Solar system 
objects are indicated by their customary symbols. The vertical lines show the masses of 
claimed planet detections, but the radii are indeterminate. The horizontal lines show the 
radii of selected low-mass stars or brown dwarfs, but the masses are uncertain. 

future. In the course of time, such observing programs will illuminate 
planet formation as an embedded process in star formation. 


First, what is a star? The mass range for stars is customarily stated 
as M. > O.OSM©, where nuclear energy generation dominates gravitational 
contraction over the stellar lifetime (Bahcall 1986). Smaller astronomical 
objects, if they are not planets, are "brown dwarfs". 

Figure 1 shows the mass and size of solar system bodies greater than 
lO-'^M©. In a restricted sense, Jupiter is a maximal planet and, indeed, 
has some stellar characteristics. Its density is approximately solar, and 
its internally generated luminosity adds about 70% to the sunlight it re- 
radiates thermally. If increased in mass, Jupiter would grow hotter and 
more self-luminous. Starlight would exert less influence over the object's 
outer characteristics. 

In the solar system, the planets' surfaces and atmospheres have prop- 
erties that are determined primarily by their distances from the Sun. Based 


narrowly on such intrinsic characteristics, an object larger than a few Jupiter 
masses could be labeled a brown dwarf because it no longer resembles a 
solar system planet. 

From the broader perspective motivated in the very first sentence, a 
planet is better defined by its origin (Black 1986). Multiple-star systems are 
thought to form by the fragmentation of spinning protostars. Generally, 
this mechanism produces elliptical orbits, and the process is not capable 
of producing bodies below a minimum mass — about O.O2M0 for solar 
metallicity (Boss 1986). A less massive secondary could form initially only 
by solid-body accretion in the special environment of a dense circumstellar 
disk (Wetherill and Stewart 1^9). By the broad view then, any object less 
than O.O2M0 is a presumptive planet 

Hubbard (1984) has discussed the class of objects sufficiently massive 
(M > O.IM0) to stabilize by deuterium burning for a brief period (~10^ 
years), but which are not stars due to the fact that they continue gravita- 
tional collapse. Van de Kamp (1986) uses a similar criterion to set Jupiter's 
mass as the upper limit to planets and the lower limit to brown dwarfs. 

Further, dynamical and physical aspects of planets are central to cur- 
rent theories of planetary system formation, such as circular orbits and 
aligned spins. These systemic aspects could provide other definitions of 
"planet" that are more directly based on the origins concept. For example, 
two O.02M0 < M < O.OSM© masses in co-planar, circular orbits around 
a star could be called a planetary system by the common-origins criterion. 
The bodies then, would be planets. Further, they might also be called brown 
dwarfs depending on scientific motivation and on whether an "origins" or 
"intrinsic" criterion were preferable for that definition. 

Finally, life originated in the solar system, and its occurrence poses a 
second fundamental question that is related hierarchically to the first posed 
above: Is the appearance of life a common by-product of planet formation? 
Perennial interest in that question suggests further restrictive criteria on 
"planets," such as a benign primary star, orbital stability, and sufficiently 
cool temperature so as not to break chemical bonds. 

Mass is the critical issue for current planet search programs, and this 
review uses mass as the discriminating factor for planets. In Figure 1, 
the mass range O.OOSM© < M < O.O2M0 is the transition zone from the 
narrow definition, meaning "not unlike solar system planets" to the broad 
definition, meaning "could not have formed like stars." 


Astronomical fight carries six dimensions of information: one each, 
spectral and temporal, and two each, spatial and polarization. In principle, 
a strategy based on any combination of these could provide evidence for 


planets around other stars, but the variations in time are most powerful: 
the fact of the orbit is confirming evidence, even if it is not the source of 
the observable effect itself. 

Any experimental design for a search program presents particular 
opportunities and impediments to the astronomer. However, all approaches 
face one problem in common: the planet's signal is always very weak, in 
both absolute and relative terms. 

Planet search techniques are either direct or indirect. Direct techniques 
use light from the planet itself. Indirect searches seek variations in starlight 
that imply the planet's presence. 

Except for the most massive planets, the main source of difficulty 
for direct detection is the planet's low intrinsic luminosity. Starlight can 
easily overwhelm planet light. (Figure 2 compares the spectral luminosity of 
Jupiter and the Sun.) For indirect searches, the problem is the planet's small 
mass or small radius. Reflex motions are proportional to the planet/star 
mass ratio, and occultation effects vary with the planet/star radius ratio 
squared. Finally, the distance from the observer gives the planet orbit a 
small angular size, which is a problem for spatial techniques, either direct 
or indirect. 

The Jupiter-Sun system is often used as a standard test example for 
planet detection schemes. Viewed from a distance of 5pc,' Jupiter would be 
26"" magnitude in the visual, and, at maximum orbital separation, it would 
be located only one arc second from a 4"* -magnitude star. This poor flux 
ratio (~10^) improves to 11.5 magnitudes (4 x W) at the wavelength of 
Jupiter's thermal spectrum peak, A = 20/zm. However, a diffraction-limited 
telescope operating at A = 20pm must be 40 times larger than an optical 
telescope in order to separate the planet and star images as effectively. 
With regard to indirect detection, the solar reflex displacement in the Sun- 
Jupiter test case is only IR© or 0.001 arc seconds at 5pc distance. The 
reflex speed is only 13 meters per second or 0.6% of the Sun's equatorial 
rotation speed. (Intrinsic stellar phenomena can also produce observational 
effects that mimic reflex motion.) Finally, if Jupiter passes in front of the 
Sun, as it does for 0.1 % of the celestial sphere for just 30 hours every 12 
years, the apparent solar flux is diminished by only 1%. 

Low signal, high background, and low information rate: these are the 
trials awaiting those who would quest for extra-solar planets. Programs to 
detect planets must be exquisitely sensitive, robust, and patient. 

^ Only about 50 stars are nearer than 5 pc, and none is closer than 1 pc 



12 - 


iS 8 

X 6 


D) 4 - 


1 cm 1mm 100|i 10|i 1^ 
■ I ■ I ■ I ■ I ■ 






I I 

I I 

8 9 10 11 12 13 14 15 16 
log Frequency (Hz) 

FIGURE 2 The specific fluxes of tlie Sun and Jupiter versus wavelength and frequency of 


With a single exception that will be discussed immediately, no inves- 
tigator has claimed a direct detection of an extra-solar planet. Therefore, 
this section's approach is to discuss the basic observational difficulties and 
the future prospects. The least massive objects that have been directly 
detected are brown dwarfs, and those observations are already described 

The exception is "VB 8B". In 1985, McCarthy et al. reported the 
detection, via infrared speckle interferometiy, of a cool (1360K) companion 
to the M dwarf star, VB 8. They stated that the observation might be the 
first direct detection of an extra-solar planet. However, subsequent star 



evolution models have shown that the described object could not have 
mass less than 0.04Mq (Nelson et al. 1986; Stringfellow 1986). More recent 
observations have failed to confirm the existence of the companion to VB 
8 (Perrier and Mariotti 1987). 

In principle, diffraction effects limit even an ideal telescope's ability to 
separate the planet image from the star image. The imperfect optics in real 
telescopes also scatter starlight into the planet image, masking its signal 
to some additional degree. For ground-based telescopes, the atmosphere 
aggravates the problem by refracting a further amount of light from the 
image core into the wings; an effect called "seeing." 

For planet searches by direct imaging, the critical instrumental factor 
is the contrast in surface brightness, which is the ratio of the brightness of 
the planet's image core to the starlight in the same region of the telescope 
focal surface. In concert with the absolute planet flux, this contrast ratio 
governs the fundamental rate at which information can accumulate about 
the planet's presence or absence. If the information rate is too low, 
systematic errors will prevent the planet's detection (Brown 1988). 

No existing long-wavelength or ground-based system offers sufficient 
contrast even to approach the direct imaging problem for extra-solar plan- 
ets. Either the Airy diffraction pattern is too wide, or seeing is, or both 
are. In the foreseeable future, only space-based telescopes operating at 
visible and near- infrared wavelengths offer a reasonable chance of success. 
(Strongly self- luminous companions, very low-mass stars and brown dwarfs, 
are an exception discussed below.) 

Free from seeing, space-based telescopes will improve the planet/star 
contrast ratio at shorter wavelengths by offering narrow, diffraction-limited 
cores. Even so, special procedures will still be needed to reduce the win^ 
of the point-spread function so that direct-imaging planet detection will be 
feasible. (Very large, very young planets are an exception and are discussed 

Figure 3 illustrates the case of the Hubble Space Tfelescope (HST). 
Brown and Burrows (1989) computed the expected HST point-spread func- 
tion and applied it to the test case, the Jupiter-Sun system viewed from 5pc. 
Because HST operates only from the ultraviolet to the near-infrared, it can 
detect only reflected starlight and not thermal radiation from a Jupiter-size 
planet. At A = 0.5/jm, figure-error scattering from the HST mirrors and 
Airy aperture diffraction contribute approximately equally to the unwanted 
background at the planet-image position.^ In this example, the predicted 
Jupiter/Sun contrast ratio is 6 x 10-^ which is unfavorable. Because of the 

^Figure error scattering dominates at larger angles or shorter wavelengths. 




,- 10 - 

• HST Parameters 

- 2.4m aperture 

- "diffraction-limited" for X>3600A 

• Jupiter and ttie Sun at 5pc distance 

- 5AU subtends 1" 

- 10% optical bandwidth: 4750-5250A 



, Airy diffraction 
PSD scattering 

6 (arc-eeconds) 



M 10 - 



" *- 0.02-. V4R - 

JO 10= - 





1 ' ' ' ' 



6 (arc-seconds) 

FIGURE 3 The contrast problem in detecting an extra-solar planet in reflecled light. The 
example is Jupiter and the Sun as seen from 5 pc. Using HST, the predicted Jupiter/Sun 
contrast ratio is 6 X 10~ , which is unfavorable. 

lengthy integration times required by information theory, and the system- 
atic problems they introduce, Brown and Burrows concluded that planet 
detection in reflected starlight is technically infeasible for HST 

The following discussion of low-mass stars and brown dwarfs is not 
complete. Its purpose is to demarcate the frontier for direct observations 
of sub-stellar objects. 

Because of their self-luminosity, the very low-mass stars are now de- 
tectable in multiple star systems using near-infrared array detectors. Becklin 
and Zuckerman (1989) have imaged an example next to the white dwarf 
GD 165. Though GD 165 is about six times hotter than the discovered 
secondary, 12,000 K vs. 2,130 K, the white dwarf is about six times smaller 
than its companion, GD 165 B. Based on the temperature and the mea- 
sured flux, the radius of GD 165 B is 0.061Rq ± O.O15R0 versus O.OIIRq 
for GD 165 A The increased surface area compensates for the temperature 
diflerence, and the two sources appear about equally strong in the near 

The mass and nature of GD 165 B are uncertain. Classically, stellar 
spectrophotometry is translated into mass using a theoretical model of 
luminosity and effective temperature versus mass and age; evolutionary 



tracks on the Hertzsprung-Russell (H-R) Diagram. Currently, though, it 
is not possible to do this confidently in the mass range 0.05Mq < M < 
O.2M0. Models predict that heavy brown dwarfs dwell for a long time 
(~10^ years) in the region of the H-R Diagram near the least massive stars 
(Nelson et al. 1986; D'Antona and Mazzitclli 1985). Furthermore, existing 
models disagree as to where the evolutionary tracks actually lie. 

Observational factors compound the confusion in using a theoretical 
mass-luminosity relationship for cool objects. Because the spectral char- 
acteristics of the cool emitting atmosphere are poorly understood, the 
reduction of the observed color temperature into an effective temperature 
is somewhat uncertain (Berriman and Reid 1984). 

Cool companions to white dwarfs can also be directly detected by spec- 
troscopy even when the image cannot be isolated. For example, Zuckerman 
and Becklin (1987) have found excess flux in the near-infrared spectrum of 
Giclas 29-38. At A = l^m, the two components have approximately equal 
signals, but the cooler source is 10 times more luminous than the white 
dwarf at A =5/jm. The color temperature of the excess flux is 1200K. In this 
case, since the secondary source has not been separately imaged, the obser- 
vations do not rule out dispersed dust as a possible source. Nevertheless, 
Zuckerman and Becklin (1987) favor the condensed source interpretation, 
"Giclas 29-38 b," for which the estimated photometric radius is O.ISRq. 

No star could conceivably be as cool as 1200K. Giclas 29-38 b would be 
a definite brown dwarf, but its mass is indeterminate in the range O.O4M0 
< M < O.O8M0. For the age of the white dwarf however, the radius of 
Giclas 29-38 b is in conflict with existing models, which predict the radius 
should be 50% smaller than observed. 

For GD 165 A/B and Giclas 29-38 a/b, the primary and secondary are 
comparably bright in a limited spectral region because the objects are very 
different. The same situation occurs, of course, in cases where the objects 
are similar, for example, very unmassive. In just such a case, Forrest et al. 
(1988) have used an infrared array detector to image a cool companion to 
the red dwarf star Gliese 569. The colors and fluxes measured by Becklin 
and Zuckerman (1989) place Gliese 569 at a hotter (2775K), more luminous 
point (O.IIRq) on the H-R diagram than GD 165 B. Because brown dwarfs 
theoretically spend much less time in their hot, luminous stage, Gliese 569 
B is more likely to be a star than GD 165 B. Nevertheless, a young age, a 
lower mass, and a brown dwarf label for Gliese 569 B are not ruled out. 

The radii of GD 165 B, Giclas 29-38 b, and Gliese 569 B are plotted 
in Figure 1. The significance of these observations for planet searches is 
two-fold. First, they exemplify the breadth and intensity of current interest 
in probing the environments of stars. Second, they show the advancing 
state of the art in cool-object spectrophotometry and the benefits of the 
new infrared array detectors. However, they have not demanded the major 


improvements in telescope imaging characteristics required by the extra- 
solar planet problem. 

If Jupiter could not be imaged at a distance of 5pc using current 
telescope systems, but a brown dwarf could, what about a large, young 
planet (Black 1980)? Consider the pair M = O.OZM© and M, = 0.35Mq 
at a mutual age of 10^ years. The planet flux would be 2% or more of 
the stellar flux longwards of A = Ifim, and with an appropriate detector, 
HST could easily detect this planet. Outside the first bright Airy ring (9 > 
0.2 arc seconds at A = Ifim), HST will suppress the image wings by >10^ 
with respect to the core. Under those conditions, the contrast ratio for this 
planet-star pair would be a favorable 20-to-l. 

Relatively unobscured T Thmi stars would be prime targets for HST to 
examine for large, young planetary companions. They have the right age, 
and they permit viewing into the immediate stellar vicinity. The young stars 
in the Taurus-Auriga dark cloud complex are at a distance 150pc, where 0.2 
arc seconds corresponds to 30AU. For these stars, HST would be expected 
to image very large planets within 10-20AU. 


Three investigator groups have claimed indirect detections of what 
may be extra-solar planets based on observed stellar reflex motions. This 
section discusses the general methods involved and the planet findings. 
Indirect detections of low-mass stars or brown dwarfs are not discussed. 

A star with a single planetary companion executes a reflex orbit that 
is isomorphic, co-planar, and synchronous with the planet orbit. The star 
orbit is smaller than the planet's by the ratio of the planet to star mass. 
If it can be detected, the star's miniature orbit implies that a second body 
exists. Further, if the star's orbit can be measured, and the star's mass 
estimated, the companion's mass and orbital radius are discovered. 

For multiple planet systems, the reflex motions are independent and 
additive in the short term. The following discussion treats the restricted 
case of a single planet in a circular orbit. 

The reflex orbit's two measurable aspects are first-order changes in 
the star's line-of-sight speed and second-order variations in its apparent 
position. (The lower-order terms are the components of normal inter- 
star motion: constant radial velocity and proper motion.) Figures 4 and 5 
explain the basic geometry, physics, and parameterizations for the two types 
of planet search based on stellar reflex motion: the astrometric search and 
the radial velocity search. 

The radial velocity and astrometric techniques produce respectively 
one- and two-dimensional data records versus time. The objective is to 
discover periodic variations in those records. 



aM =a,M, 



1^=1, a^=1,V5, =29.8 kms' 

Kepler's Third Law 

IV. sin i 

Measurement Interpretation: 

• Determine M^trom star's spectral class 

• Adopt an assumption about sin i, 

e.g.. sin i - 1 . 

• Compute: 


log a 
Semi-Major Axis (AU) 

FIGURE 4 A tutorial on the radial velocity technique for indirectly detecting extra-solar 

The Scargle periodogram (1982; Home and Baliunas 1986) is a stan- 
dard procedure to discover and assign statistical significance to periodic 
signals. Black and Scargle (1982) have discussed it in the context of as- 
trometry, and their mathematical results also apply to the radial velocity 
approach. The detection efficiency, for example, is the key to knowing the 
minimum detectable signal and for interpreting null results. 

For long periods, where the observations may cover only about one 
cycle, the periodogram's performance needs to be better understood in 
purely mathematical terms.^ Black and Scargle (1982) have also identified 
a potential source of systematic error in the long-period regime due to 
incorrect accommodation of linear drifts. Because long periods are asso- 
ciated with wide orbits, these factors further impede drawing valid early 
results from planet searches. 

In practice, systematic rather than random errors may determine the 

^Home and Baliunas remark on page 761, "clear arrow signals with period slightly longer 
than T can sometimes be detected, but with poor resolution." 





r-r . 




aM-a.M, Physics 


Mg-1 . a9=1,D,pc.1.e,-.1 Normalization 


Kepler's Third Law 

Determine D from the star's annual parallax 
{assume 0-1 Ope tor -1 00 candidate stars) 




-9. a 



log a 
Semi-Major Axis (AU) 

FIGURE 5 A tutorial on the aslrometric technique for indirectly detecting extra-solar 

minimum detectable signal in reflex motion searches. The systematic er- 
rors may be real variabilities of the star (Gilliland and Baliunas 1987) or 
limitations of the instruments. As a class, systematic errors demand the 
planet searcher's assiduous attention. 

Once detected, the amplitude of the reflex signal, V, or 0^, and its 
period, r, provide specific information about the planetary mass and semi- 
major axis. The graduated lines in the graphs in Figures 4 and 5 signify the 
interpretation. The star's mass is required, and for main sequence stars, M, 
can be determined adequately from the stellar-spectral type. For evolved 
stars, the mass assignment is more uncertain. 

The radial velocity amplitude, V., is independent of Earth-star dis- 
tance. The true orbital speed is V,/sin(i), where the orbit's inclination 
angle, i, with respect to the line of sight is unknown unless it is determined 
separately. The average value of sin(i) in a random sample is 0.79. 

The astrometric amplitude, 0,, is a two-dimensional vector with com- 
ponents of right ascension and declination. When viewed from an inclined 
angle, a circular orbit is an apparent ellipse on the celestial sphere. In 
principle, the secular motion of the star along this elliptical path uniquely 
determines the true orbit, including the inclination angle. 



FIT: y,= 25 m/s, X = 2.6 years 

1981 1982 1983 1984 1985 1986 1987 1988 

FIGURE 6 The dala for the "probable" deteclion claimed by Campbell et al. of a 
planetary companion to 7 Cephei. 

Campbell et al. (1988) have conducted a search program that measured 
the radial velocities of 15 stars for six years with a precision of about 10 
meters per second. The authors report statistically significant, long-term 
accelerations for seven stars, and in one case, they claim the "probable" 
detection of a period. The A Cephei observations, with a large quadratic 
drift subtracted, are shown in Figure 6. The investigators have fitted a sine 
wave with amplitude V, = 25 meters per second and period t = 2.6 years 
to the data. 

7 Cephei is classed as spectral type Kl III-IV, indicating it has evolved 
far from the main sequence on the HR diagram. The rather uncertain mass 
estimate is M. = 1.15 ± O.IM© Therefore, the period implies an orbital 
semi-major axis a = 2AU, which subtends 0.13 arc seconds at the 15pc 
distance of 7 Cephei. Assuming the orbit is viewed edge-on, the implied 
mass for 7 Cephei b is M = 1.3 x lO-^M©. 

Figure 7 shows a radial velocity detection by Latham et al. (1989) 
which has been confirmed independently by the CORAVEL program. For 
the low-metal, but otherwise solar-type star HD 114762, the Center for 
Astrophysics team obtained 208 measurements with a typical precision of 



FIT: V^ 0.551 ±0.42 km/s, T = 84.0±0.1 days 

I 1 1 1 r 

+1.0 - 

J 0.0 



FIGURE 7 The data for the detection claimed by Latham el al. for a planetary companion 
HDl 14762. 

0.4 kilometers per second over a 12-year inierval. A periodogram analysis 
indicates a highly significant signal with period r = 84 ± 0.1 days and 
amplitude V, = 0.551 ± 0.042 kilometers per second. The best fit is not 
a pure sine wave, which may indicate either an elliptical orbit or another 
orbiting body. 

Estimating the mass of HDl 14762 at M, = IMq, the short period 
indicates an orbit like Mercury's: a = 0.38AU. At the 28pc distance of this 
system, the estimated semi-major axis subtends 0.14 arc seconds. Assuming 
a sin0e orbit is viewed edge-on, the implied mass for HD114762 b is M = 
1.1 X lO-^M©. 

Van de Kamp (1986) claims the detection of two planets in his astro- 
metric record of Barnard's star, which is shown in Figure 8. Barnard's star 
is late-type M dwarf, which is faint (m^ - 9.5), although close (1.8pc). Van 
de Kamp fits his data with two amplitude-period combinations: (0.0070 arc 




eji)=0.0070", T(i) = 12yrs 
e,{2) =0.0064? x(2) =20 yrs 

+0.03 r 


+0.03* r 





-I 1960 0-- 


Barnard's Star 

1970 -■ 

1 , — 1980.0 



• • " 





FIGURE 8 The data for the detection claimed by van de Kamp for two planetary 
companions to Barnard's Star. 

seconds, 12 years) and (0.0064 arc seconds, 20 years). Estimating the mass 
of Barnard's star at O.14M0, the semi-major axes are aj = 2.7AU and a^ = 
3.8AU. (For the astrometric technique, the semi-major axis is independent 
of the system's inclination angle.) The masses derived for the companions 
are Mj = 6.6 x 10-^Mq and M,, = 4.2 x 10-''Mo. 

The van de Kamp observations extend over more than 40 years, and 
they have been widely discussed and disputed. The independent observa- 
tions of Barnard's star shown by Harrington and Harrington (1987) are not 
consistent with the orbit solution by van de Kamp. 


Three investigator groups have reported detecting objects that are 
candidates for extra-solar planets according to the broad definition of the 
term based on mass. The findings are summarized in Figure 9. 

All three claimed planet detections are based on stellar reflex motions, 
an indirect method. Searches based on direct imaging are currently limited 
to brown dwarfs because smaller objects are not sufficiently luminous to 
overcome scattered starlight. 

Latham et a/.'s (1989) detection of HD114762 b is solid. If the orbit 
is viewed edge-on, this object has a mass about 10 times that of Jupiter 
and is a planet by the definition adopted in this review. However, the 
inclination angle of the orbit is uncertain, and if sin(i) is small, the edge-on 
assumption would cause the actual mass of HD114762 b to be significantly 
underestimated. On an a priori basis, though, this is improbable. More 
radial velocity observations will clarify whether the departure of HD114762 











-7 J 


HD11 4762 b 

Barnard b 
Barnard c 

■ 2L 


-1 +1 

log a (AU) 


FIGURE 9 Summary of currently claimed extra-solar planet detections plotted versus 
orbital semi-major axis and mass. 

b's radial velocity variations from a sine curve implies a non-circular orbit 
or a second orbiting body. 

7 Cephei b and the companions to Barnard's Star are uncertain. More 
measurements over a longer time base are needed to confirm or deny their 


The technological frontier for extra-solar planet detection lies in space- 
based systems. While the radial velocity approach is operating near the 
limits set by stellar atmospheric effects, the high-image quality potentially 
available in space will greatly benefit other search techniques (Borucki et 
al. 1988; Tferrile 1988; Levy et al. 1988). 

Regarding the future for extra-solar planet observations, Marcy and 
Moore (1989) offer a glimpse that is deceptively simple in a subtle way. 
They synthesize radial velocity, astrometric, and photometric studies of the 
low-mass (O.OeVM© < M < O.OSTM©) companion of Gliese 623. These 


data sets arc independent and complementary. Analyzed together, the 
measurements reveal a rich picture of the object, with regard to the special 
capabilities of the individual observing techniques. As a scientific bonus, 
the result challenges theory: the luminosity of Gliese 623 B is significantly 
greater than is predicted by current models for stars of its mass and age. 

Liebert and Probst (1987) have reviewed the scientific issues for low- 
mass stars and brown dwarfs. For those objects, the key scientific questions 
are about their total numbers and their intrinsic properties. The issues 
are not systemic, and current observing approaches address the critical 
questions, as Marcy and Moore show. 

The scientific issues for extra-solar planets are qualitatively different 
from those for low-mass stars and brown dwarfs, lb understand the origin 
and evolution of the solar system in the context of the astronomical record, 
systems of extra-solar planets must be studied as such. That means finding 
and understanding multiple planets per star, because only then can systemic 
aspects can be measured. 

This review has really discussed the observational progress toward 
"the existence theorem:" discovering just the first extra-solar planets. Mea- 
suring the joint properties of multiple-planetary systems is a qualitatively 
more difficult challenge that will demand major technological advances. 
Nevertheless, this goal has durable importance for planetary science. 

Someday, with much investment, work, and care, incisive observations 
of extra-solar planetary systems will challenge our theories and ideas about 
the solar system's formation and evolution. 


The author gratefully acknowledges the thoughtful and helpful com- 
ments on the manuscript by D. Black, C. Burrows, R. Gilliland, D. Latham, 
D. Soderblom, and H. Weaver. This work was supported by NASA through 
Contract NAS5-26555 with the Space Tfelescope Science Institute, which is 
operated by AURA, Inc. 


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Appendix I 
List of Participants 

University of Michigan 

Institute of Space Research 


Vernadskiy Institute of Geochemistry and Analytical Chemistry 

University of California, Santa Cruz 


Carnegie Institution of Washington 


Space Telescope Science Institute 

University of Minnesota 

Institute of Space Research 

Atmospheric Physics Institute 

University of Arizona 





The Pennsylvania State University 


Schmidt Institute of the Physics of the Earth 


Vernadskiy Institute of Geochemistry and Analytical Chemistry 

University of Arizona 

Institute of Space Research 

Institute of Space Research 


Shirshov Institute of Oceanology 

Institute of Space Research 


Institute of Space Research 

Massachusetts Institute of Tfechnology 


Schmidt Institute of the Physics of the Earth 


Schmidt Institute of the Physics of the Earth 

California Institute of Tfechnology 


Schmidt Institute of the Physics of the Earth 


Vernadskiy Institute of Geochemistry and Analytical Chemistry 

University of Michigan 

Planetary Sciences Institute 

Carnegie Institution of Washington 


Vernadskiy Institute of Geochemistry and Analytical Chemistry 


Institute of Experimental Mineralogy 


Schmidt Institute of the Physics of the Earth 


Appendix II 
List of Presentations 


P. Bodenheimer (University of California, Santa Cruz) "Numerical 

"Bvo-Dimensional Calculations of the Formation of the Solar Nebula" 
A. Boss (Carnegie Institution of Washington) "Three-Dimensional 

Evolution of the Early Solar Nebula" 
R. Brown (Space Tfelescope Science Institute) "Progress in Extra-Solar 

Planet Detection" 
R. Gehrz (University of Minnesota) "Astrophysical Dust Grains in Stars, 

the Interstellar Medium, and the Solar System" 
J. Kasting (Pennsylvania State University) "Runaway Greenhouse 

Atmospheres: Applications to Earth and Venus" 
E. Levy (University of Arizona) "Magnetohydrodynamic Puzzles in the 

Protoplanetary Nebula" 
R. Pepin (University of Minnesota) "Mass Fractionation and 

Hydrodynamic Escape" (Presented by D. Hunlen) 
D. Stevenson (California Institute of Technology) "Giant Planets and 

Their Satellites: What are the Relationships Between Their 

Properties and How They Formed?" 
S. Strom (University of Massachusetts, Amherst) "Astrophysical 

Constraints on the Time Scale for Planet Building" (Presented by T. 

Donahue and R. Brown) 
J. Walker (University of Michigan) "Degassing" 
S. Weidenschilling (Planetary Sciences Institute) "Formation of 




G. Wetherill (Carnegie Institution of Washington) "Formation of the 
Ttrrestrial Planets from Planetesimals" 


A. Basilyevskiy (Vernadskiy Institute of Geochemistry and Analytical 

Chemistry) "Venus Geology" 
A. Lavrukhina (Vernadskiy Institute of Geochemistry and Analytical 

Chemistry) "Physical and Chemical Processes at Early Stages of 

Protoplanetary Nebula Evolution" 

V Linkin (Institute of Space Research) "Dynamics and Thermal Structure 

of the Venusian Atmosphere" 
L. Marochnik (Institute of Space Research) "The Oort Cloud" 
V. Moroz (Institute of Space Research) "Mars: Evolution of Climate and 

L. Mukhin, M. Gerasimov (Institute of Space Research) "The Role of 

Impact Processes in the Chemical Evolution of the Atmosphere of 

Primordial Earth" 
T. Ruzmaikina, A. Makalkin (Schmidt Institute of the Physics of the 

Earth) "Origin and Evolution of Protoplanetary Discs" 

V Safronov (Schmidt Institute of the Physics of the Earth) "Small Bodies 

of the Solar System and the Rate of Planet Formation" 
A. Vityazev, G. Pechernikova (Schmidt Institute of the Physics of the 

Earth) "The Latest Stage of Accumulation and the Initial Evolution 

of Planetary Resources" 
V. Volkov (Vernadskiy Institute of Geochemistry and Analytical 

Chemistry) "Interaction Between Lithosphere and Atmosphere on 

G. Zaslavskiy (Vernadskiy Institute of Geochemistry and Analytical 

Chemistry) "Dynamic Stochasticity of Comets Coming from the Oort 

Cloud and Numeric Simulation" 

V Zharkov, V Solomatov (Schmidt Institute of the Physics of the Earth) 

"Thermal Regime on Venus"